5,015,340 and 0: Calculate all the common factors (divisors) of the two numbers (and the prime factors)

The common factors (divisors) of the numbers 5,015,340 and 0

The common factors (divisors) of the numbers 5,015,340 and 0 are all the factors of their 'greatest (highest) common factor (divisor)'.

To remember:

A factor (divisor) of a natural number A is a natural number B which when multiplied by another natural number C equals the given number A:
A = B × C. Example: 60 = 2 × 30.

Both B and C are factors of A and they both evenly divide A ( = without a remainder).

Calculate the greatest (highest) common factor (divisor), gcf, hcf, gcd:

gcf, hcf, gcd (0; n1) = n1, where n1 is a natural number.

gcf, hcf, gcd (5,015,340; 0) = 5,015,340

Zero is divisible by any number other than zero (there is no remainder when dividing zero by these numbers)

>> The greatest (highest) common factor (divisor)

Preliminary step to take before finding all the factors:

To find all the factors (all the divisors) of the 'gcf', we need to break 'gcf' down into its prime factors (to build its prime factorization, to decompose it into prime factors, to write it as a product of prime numbers).

The prime factorization of the greatest (highest) common factor (divisor):

The prime factorization of a number (the decomposition of the number into prime factors, breaking down the number into prime numbers): finding the prime numbers that multiply together to make that number.

5,015,340 = 2² × 3² × 5 × 11 × 17 × 149
5,015,340 is not a prime number but a composite one.

* The natural numbers that are divisible only by 1 and themselves are called prime numbers. A prime number has exactly two factors: 1 and itself.
* A composite number is a natural number that has at least one other factor than 1 and itself.

>> The prime factorization

Find all the factors (divisors) of the greatest (highest) common factor (divisor), gcf, hcf, gcd

Multiply the prime factors involved in the prime factorization of the GCF in all their unique combinations, that give different results.

gcf, hcf, gcd = 5,015,340 = 2² × 3² × 5 × 11 × 17 × 149

Also consider the exponents of the prime factors (example: 3² = 3 × 3 = 9).

Also add 1 to the list of factors (divisors). All the numbers are divisible by 1.

All the factors (divisors) are listed below - in ascending order

The list of factors (divisors):

neither prime nor composite = 1

prime factor = 2

prime factor = 3

2² = 4

prime factor = 5

2 × 3 = 6

3² = 9

2 × 5 = 10

prime factor = 11

2² × 3 = 12

3 × 5 = 15

prime factor = 17

2 × 3² = 18

2² × 5 = 20

2 × 11 = 22

2 × 3 × 5 = 30

3 × 11 = 33

2 × 17 = 34

2² × 3² = 36

2² × 11 = 44

3² × 5 = 45

3 × 17 = 51

5 × 11 = 55

2² × 3 × 5 = 60

2 × 3 × 11 = 66

2² × 17 = 68

5 × 17 = 85

2 × 3² × 5 = 90

3² × 11 = 99

2 × 3 × 17 = 102

2 × 5 × 11 = 110

2² × 3 × 11 = 132

prime factor = 149

3² × 17 = 153

3 × 5 × 11 = 165

2 × 5 × 17 = 170

2² × 3² × 5 = 180

11 × 17 = 187

2 × 3² × 11 = 198

2² × 3 × 17 = 204

2² × 5 × 11 = 220

3 × 5 × 17 = 255

2 × 149 = 298

2 × 3² × 17 = 306

2 × 3 × 5 × 11 = 330

2² × 5 × 17 = 340

2 × 11 × 17 = 374

2² × 3² × 11 = 396

3 × 149 = 447

3² × 5 × 11 = 495

2 × 3 × 5 × 17 = 510

3 × 11 × 17 = 561

2² × 149 = 596

2² × 3² × 17 = 612

2² × 3 × 5 × 11 = 660

5 × 149 = 745

2² × 11 × 17 = 748

3² × 5 × 17 = 765

2 × 3 × 149 = 894

5 × 11 × 17 = 935

2 × 3² × 5 × 11 = 990

2² × 3 × 5 × 17 = 1,020

2 × 3 × 11 × 17 = 1,122

3² × 149 = 1,341

2 × 5 × 149 = 1,490

2 × 3² × 5 × 17 = 1,530

11 × 149 = 1,639

3² × 11 × 17 = 1,683

2² × 3 × 149 = 1,788

2 × 5 × 11 × 17 = 1,870

2² × 3² × 5 × 11 = 1,980

3 × 5 × 149 = 2,235

This list continues below...

... This list continues from above

2² × 3 × 11 × 17 = 2,244

17 × 149 = 2,533

2 × 3² × 149 = 2,682

3 × 5 × 11 × 17 = 2,805

2² × 5 × 149 = 2,980

2² × 3² × 5 × 17 = 3,060

2 × 11 × 149 = 3,278

2 × 3² × 11 × 17 = 3,366

2² × 5 × 11 × 17 = 3,740

2 × 3 × 5 × 149 = 4,470

3 × 11 × 149 = 4,917

2 × 17 × 149 = 5,066

2² × 3² × 149 = 5,364

2 × 3 × 5 × 11 × 17 = 5,610

2² × 11 × 149 = 6,556

3² × 5 × 149 = 6,705

2² × 3² × 11 × 17 = 6,732

3 × 17 × 149 = 7,599

5 × 11 × 149 = 8,195

3² × 5 × 11 × 17 = 8,415

2² × 3 × 5 × 149 = 8,940

2 × 3 × 11 × 149 = 9,834

2² × 17 × 149 = 10,132

2² × 3 × 5 × 11 × 17 = 11,220

5 × 17 × 149 = 12,665

2 × 3² × 5 × 149 = 13,410

3² × 11 × 149 = 14,751

2 × 3 × 17 × 149 = 15,198

2 × 5 × 11 × 149 = 16,390

2 × 3² × 5 × 11 × 17 = 16,830

2² × 3 × 11 × 149 = 19,668

3² × 17 × 149 = 22,797

3 × 5 × 11 × 149 = 24,585

2 × 5 × 17 × 149 = 25,330

2² × 3² × 5 × 149 = 26,820

11 × 17 × 149 = 27,863

2 × 3² × 11 × 149 = 29,502

2² × 3 × 17 × 149 = 30,396

2² × 5 × 11 × 149 = 32,780

2² × 3² × 5 × 11 × 17 = 33,660

3 × 5 × 17 × 149 = 37,995

2 × 3² × 17 × 149 = 45,594

2 × 3 × 5 × 11 × 149 = 49,170

2² × 5 × 17 × 149 = 50,660

2 × 11 × 17 × 149 = 55,726

2² × 3² × 11 × 149 = 59,004

3² × 5 × 11 × 149 = 73,755

2 × 3 × 5 × 17 × 149 = 75,990

3 × 11 × 17 × 149 = 83,589

2² × 3² × 17 × 149 = 91,188

2² × 3 × 5 × 11 × 149 = 98,340

2² × 11 × 17 × 149 = 111,452

3² × 5 × 17 × 149 = 113,985

5 × 11 × 17 × 149 = 139,315

2 × 3² × 5 × 11 × 149 = 147,510

2² × 3 × 5 × 17 × 149 = 151,980

2 × 3 × 11 × 17 × 149 = 167,178

2 × 3² × 5 × 17 × 149 = 227,970

3² × 11 × 17 × 149 = 250,767

2 × 5 × 11 × 17 × 149 = 278,630

2² × 3² × 5 × 11 × 149 = 295,020

2² × 3 × 11 × 17 × 149 = 334,356

3 × 5 × 11 × 17 × 149 = 417,945

2² × 3² × 5 × 17 × 149 = 455,940

2 × 3² × 11 × 17 × 149 = 501,534

2² × 5 × 11 × 17 × 149 = 557,260

2 × 3 × 5 × 11 × 17 × 149 = 835,890

2² × 3² × 11 × 17 × 149 = 1,003,068

3² × 5 × 11 × 17 × 149 = 1,253,835

2² × 3 × 5 × 11 × 17 × 149 = 1,671,780

2 × 3² × 5 × 11 × 17 × 149 = 2,507,670

2² × 3² × 5 × 11 × 17 × 149 = 5,015,340

The final answer:
(scroll down)

5,015,340 and 0 have 144 common factors (divisors):
1; 2; 3; 4; 5; 6; 9; 10; 11; 12; 15; 17; 18; 20; 22; 30; 33; 34; 36; 44; 45; 51; 55; 60; 66; 68; 85; 90; 99; 102; 110; 132; 149; 153; 165; 170; 180; 187; 198; 204; 220; 255; 298; 306; 330; 340; 374; 396; 447; 495; 510; 561; 596; 612; 660; 745; 748; 765; 894; 935; 990; 1,020; 1,122; 1,341; 1,490; 1,530; 1,639; 1,683; 1,788; 1,870; 1,980; 2,235; 2,244; 2,533; 2,682; 2,805; 2,980; 3,060; 3,278; 3,366; 3,740; 4,470; 4,917; 5,066; 5,364; 5,610; 6,556; 6,705; 6,732; 7,599; 8,195; 8,415; 8,940; 9,834; 10,132; 11,220; 12,665; 13,410; 14,751; 15,198; 16,390; 16,830; 19,668; 22,797; 24,585; 25,330; 26,820; 27,863; 29,502; 30,396; 32,780; 33,660; 37,995; 45,594; 49,170; 50,660; 55,726; 59,004; 73,755; 75,990; 83,589; 91,188; 98,340; 111,452; 113,985; 139,315; 147,510; 151,980; 167,178; 227,970; 250,767; 278,630; 295,020; 334,356; 417,945; 455,940; 501,534; 557,260; 835,890; 1,003,068; 1,253,835; 1,671,780; 2,507,670 and 5,015,340
out of which 6 prime factors: 2; 3; 5; 11; 17 and 149

A quick way to find the factors (the divisors) of a number is to first have its prime factorization.

Then multiply the prime factors in all the possible combinations that lead to different results and also take into account their exponents, if any.

The latest 5 sets of calculated factors (divisors): of one number or the common factors of two numbers

The common factors (divisors) of 5,015,340 and 0 = ?	Mar 25 14:17 UTC (GMT)
The common factors (divisors) of 8,576,400 and 0 = ?	Mar 25 14:17 UTC (GMT)
The factors (divisors) of 1,550,359 = ?	Mar 25 14:16 UTC (GMT)
The common factors (divisors) of 270 and 378 = ?	Mar 25 14:16 UTC (GMT)
The factors (divisors) of 1,365,936 = ?	Mar 25 14:16 UTC (GMT)
The list of all the calculated factors (divisors) of one or two numbers

Calculate all the divisors (factors) of the given numbers

How to calculate (find) all the factors (divisors) of a number:

Break down the number into prime factors. Then multiply its prime factors in all their unique combinations, that give different results.

To calculate the common factors of two numbers:

The common factors (divisors) of two numbers are all the factors of the greatest common factor, gcf.

Calculate the greatest (highest) common factor (divisor) of the two numbers, gcf (hcf, gcd).

Break down the GCF into prime factors. Then multiply its prime factors in all their unique combinations, that give different results.

Factors (divisors), common factors (common divisors), the greatest common factor, GCF (also called the greatest common divisor, GCD, or the highest common factor, HCF)

If the number "t" is a factor (divisor) of the number "a" then in the prime factorization of "t" we will only encounter prime factors that also occur in the prime factorization of "a".
If there are exponents involved, the maximum value of an exponent for any base of a power that is found in the prime factorization of "t" (powers, or multiplicities) is at most equal to the exponent of the same base that is involved in the prime factorization of "a".
Hint: 2³ = 2 × 2 × 2 = 8. 2 is called the base and 3 is the exponent. 2³ is the power and 8 is the value of the power. We sometimes say that the number 2 is raised to the power of 3.

For example, 12 is a factor (divisor) of 120 - the remainder is zero when dividing 120 by 12.
Let's look at the prime factorization of both numbers and notice the bases and the exponents that occur in the prime factorization of both numbers:
12 = 2 × 2 × 3 = 2² × 3
120 = 2 × 2 × 2 × 3 × 5 = 2³ × 3 × 5
120 contains all the prime factors of 12, and all its bases' exponents are higher than those of 12.

If "t" is a common factor (divisor) of "a" and "b", then the prime factorization of "t" contains only the common prime factors involved in the prime factorizations of both "a" and "b".
If there are exponents involved, the maximum value of an exponent for any base of a power that is found in the prime factorization of "t" is at most equal to the minimum of the exponents of the same base that is involved in the prime factorization of both "a" and "b".

For example, 12 is the common factor of 48 and 360.
The remainder is zero when dividing either 48 or 360 by 12.
Here there are the prime factorizations of the three numbers, 12, 48 and 360:
12 = 2² × 3
48 = 2⁴ × 3
360 = 2³ × 3² × 5
Please note that 48 and 360 have more factors (divisors): 2, 3, 4, 6, 8, 12, 24. Among them, 24 is the greatest common factor, GCF (or the greatest common divisor, GCD, or the highest common factor, HCF) of 48 and 360.

The greatest common factor, GCF, of two numbers, "a" and "b", is the product of all the common prime factors involved in the prime factorizations of both "a" and "b", taken by the lowest exponents.
Based on this rule it is calculated the greatest common factor, GCF, (or the greatest common divisor GCD, HCF) of several numbers, as shown in the example below...

GCF, GCD (1,260; 3,024; 5,544) = ?
1,260 = 2² × 3²
3,024 = 2⁴ × 3² × 7
5,544 = 2³ × 3² × 7 × 11
The common prime factors are:
2 - its lowest exponent (multiplicity) is: min.(2; 3; 4) = 2
3 - its lowest exponent (multiplicity) is: min.(2; 2; 2) = 2
GCF, GCD (1,260; 3,024; 5,544) = 2² × 3² = 252

Coprime numbers:
If two numbers "a" and "b" have no other common factors (divisors) than 1, gfc, gcd, hcf (a; b) = 1, then the numbers "a" and "b" are called coprime (or relatively prime).

Factors of the GCF
If "a" and "b" are not coprime, then every common factor (divisor) of "a" and "b" is a also a factor (divisor) of the greatest common factor, GCF (greatest common divisor, GCD, highest common factor, HCF) of "a" and "b".