985,920 and 0: Calculate all the common factors (divisors) of the two numbers (and the prime factors)

The common factors (divisors) of the numbers 985,920 and 0

The common factors (divisors) of the numbers 985,920 and 0 are all the factors of their 'greatest (highest) common factor (divisor)'.

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. 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 (985,920; 0) = 985,920

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

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

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

The prime factorization of a number: finding the prime numbers that multiply together to make that number.

985,920 = 2⁶ × 3 × 5 × 13 × 79
985,920 is not a prime number but a composite one.

* The natural numbers that are only divisible 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

985,920 = 2⁶ × 3 × 5 × 13 × 79

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

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

2³ = 8

2 × 5 = 10

2² × 3 = 12

prime factor = 13

3 × 5 = 15

2⁴ = 16

2² × 5 = 20

2³ × 3 = 24

2 × 13 = 26

2 × 3 × 5 = 30

2⁵ = 32

3 × 13 = 39

2³ × 5 = 40

2⁴ × 3 = 48

2² × 13 = 52

2² × 3 × 5 = 60

2⁶ = 64

5 × 13 = 65

2 × 3 × 13 = 78

prime factor = 79

2⁴ × 5 = 80

2⁵ × 3 = 96

2³ × 13 = 104

2³ × 3 × 5 = 120

2 × 5 × 13 = 130

2² × 3 × 13 = 156

2 × 79 = 158

2⁵ × 5 = 160

2⁶ × 3 = 192

3 × 5 × 13 = 195

2⁴ × 13 = 208

3 × 79 = 237

2⁴ × 3 × 5 = 240

2² × 5 × 13 = 260

2³ × 3 × 13 = 312

2² × 79 = 316

2⁶ × 5 = 320

2 × 3 × 5 × 13 = 390

5 × 79 = 395

2⁵ × 13 = 416

2 × 3 × 79 = 474

2⁵ × 3 × 5 = 480

2³ × 5 × 13 = 520

2⁴ × 3 × 13 = 624

2³ × 79 = 632

2² × 3 × 5 × 13 = 780

2 × 5 × 79 = 790

2⁶ × 13 = 832

2² × 3 × 79 = 948

2⁶ × 3 × 5 = 960

This list continues below...

... This list continues from above

13 × 79 = 1,027

2⁴ × 5 × 13 = 1,040

3 × 5 × 79 = 1,185

2⁵ × 3 × 13 = 1,248

2⁴ × 79 = 1,264

2³ × 3 × 5 × 13 = 1,560

2² × 5 × 79 = 1,580

2³ × 3 × 79 = 1,896

2 × 13 × 79 = 2,054

2⁵ × 5 × 13 = 2,080

2 × 3 × 5 × 79 = 2,370

2⁶ × 3 × 13 = 2,496

2⁵ × 79 = 2,528

3 × 13 × 79 = 3,081

2⁴ × 3 × 5 × 13 = 3,120

2³ × 5 × 79 = 3,160

2⁴ × 3 × 79 = 3,792

2² × 13 × 79 = 4,108

2⁶ × 5 × 13 = 4,160

2² × 3 × 5 × 79 = 4,740

2⁶ × 79 = 5,056

5 × 13 × 79 = 5,135

2 × 3 × 13 × 79 = 6,162

2⁵ × 3 × 5 × 13 = 6,240

2⁴ × 5 × 79 = 6,320

2⁵ × 3 × 79 = 7,584

2³ × 13 × 79 = 8,216

2³ × 3 × 5 × 79 = 9,480

2 × 5 × 13 × 79 = 10,270

2² × 3 × 13 × 79 = 12,324

2⁶ × 3 × 5 × 13 = 12,480

2⁵ × 5 × 79 = 12,640

2⁶ × 3 × 79 = 15,168

3 × 5 × 13 × 79 = 15,405

2⁴ × 13 × 79 = 16,432

2⁴ × 3 × 5 × 79 = 18,960

2² × 5 × 13 × 79 = 20,540

2³ × 3 × 13 × 79 = 24,648

2⁶ × 5 × 79 = 25,280

2 × 3 × 5 × 13 × 79 = 30,810

2⁵ × 13 × 79 = 32,864

2⁵ × 3 × 5 × 79 = 37,920

2³ × 5 × 13 × 79 = 41,080

2⁴ × 3 × 13 × 79 = 49,296

2² × 3 × 5 × 13 × 79 = 61,620

2⁶ × 13 × 79 = 65,728

2⁶ × 3 × 5 × 79 = 75,840

2⁴ × 5 × 13 × 79 = 82,160

2⁵ × 3 × 13 × 79 = 98,592

2³ × 3 × 5 × 13 × 79 = 123,240

2⁵ × 5 × 13 × 79 = 164,320

2⁶ × 3 × 13 × 79 = 197,184

2⁴ × 3 × 5 × 13 × 79 = 246,480

2⁶ × 5 × 13 × 79 = 328,640

2⁵ × 3 × 5 × 13 × 79 = 492,960

2⁶ × 3 × 5 × 13 × 79 = 985,920

The final answer:
(scroll down)

985,920 and 0 have 112 common factors (divisors):
1; 2; 3; 4; 5; 6; 8; 10; 12; 13; 15; 16; 20; 24; 26; 30; 32; 39; 40; 48; 52; 60; 64; 65; 78; 79; 80; 96; 104; 120; 130; 156; 158; 160; 192; 195; 208; 237; 240; 260; 312; 316; 320; 390; 395; 416; 474; 480; 520; 624; 632; 780; 790; 832; 948; 960; 1,027; 1,040; 1,185; 1,248; 1,264; 1,560; 1,580; 1,896; 2,054; 2,080; 2,370; 2,496; 2,528; 3,081; 3,120; 3,160; 3,792; 4,108; 4,160; 4,740; 5,056; 5,135; 6,162; 6,240; 6,320; 7,584; 8,216; 9,480; 10,270; 12,324; 12,480; 12,640; 15,168; 15,405; 16,432; 18,960; 20,540; 24,648; 25,280; 30,810; 32,864; 37,920; 41,080; 49,296; 61,620; 65,728; 75,840; 82,160; 98,592; 123,240; 164,320; 197,184; 246,480; 328,640; 492,960 and 985,920
out of which 5 prime factors: 2; 3; 5; 13 and 79

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 985,920 and 0 = ?	Jul 03 05:35 UTC (GMT)
The factors (divisors) of 2,591,827 = ?	Jul 03 05:35 UTC (GMT)
The factors (divisors) of 74,469,780 = ?	Jul 03 05:35 UTC (GMT)
The common factors (divisors) of 14,819,112,003 and 0 = ?	Jul 03 05:35 UTC (GMT)
The factors (divisors) of 332,940 = ?	Jul 03 05:35 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".