Given the Number 892,320, Calculate (Find) All the Factors (All the Divisors) of the Number 892,320 (the Proper, the Improper and the Prime Factors)

The factors (divisors) of the number 892,320

892,320 is a composite number and can be prime factorized.

So what are all the factors (divisors) of the number 892,320?

A factor (a divisor) of the number 892,320 is a natural number B which when multiplied by another natural number C equals the given number 892,320:
892,320 = B × C. Example: 60 = 2 × 30.

Both B and C are factors of 892,320.

To find all the factors (divisors) of the number 892,320:

1) Break down the number into its prime factors (build the number's prime factorization, decompose it into prime factors, write it as a product of prime numbers).

2) Then multiply these prime factors in all their unique combinations, that yield different results.

1) The prime factorization:

The prime factorization of the number 892,320 (the decomposition of the number into prime factors, breaking the number down into prime numbers) = dividing the number 892,320 into smaller, prime numbers. The number 892,320 results from the multiplication of these prime numbers.

892,320 = 2⁵ × 3 × 5 × 11 × 13²
892,320 is not a prime number but a composite one.

* The natural numbers that are divisible (that are divided evenly) only by 1 and themselves are called prime numbers. Examples: 2, 3, 5, 7, 11, 13, 17. A prime number has exactly two factors: 1 and the number itself.
* A composite number is a natural number that has at least one factor other than 1 and itself. Examples: 4, 6, 8, 9, 10, 12, 14.

>> Prime numbers. Composite Numbers. Prime factorization

2) How do I find all the factors (divisors) of the number?

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

892,320 = 2⁵ × 3 × 5 × 11 × 13²

Also consider the exponents of these prime factors.

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

prime factor = 11

2² × 3 = 12

prime factor = 13

3 × 5 = 15

2⁴ = 16

2² × 5 = 20

2 × 11 = 22

2³ × 3 = 24

2 × 13 = 26

2 × 3 × 5 = 30

2⁵ = 32

3 × 11 = 33

3 × 13 = 39

2³ × 5 = 40

2² × 11 = 44

2⁴ × 3 = 48

2² × 13 = 52

5 × 11 = 55

2² × 3 × 5 = 60

5 × 13 = 65

2 × 3 × 11 = 66

2 × 3 × 13 = 78

2⁴ × 5 = 80

2³ × 11 = 88

2⁵ × 3 = 96

2³ × 13 = 104

2 × 5 × 11 = 110

2³ × 3 × 5 = 120

2 × 5 × 13 = 130

2² × 3 × 11 = 132

11 × 13 = 143

2² × 3 × 13 = 156

2⁵ × 5 = 160

3 × 5 × 11 = 165

13² = 169

2⁴ × 11 = 176

3 × 5 × 13 = 195

2⁴ × 13 = 208

2² × 5 × 11 = 220

2⁴ × 3 × 5 = 240

2² × 5 × 13 = 260

2³ × 3 × 11 = 264

2 × 11 × 13 = 286

2³ × 3 × 13 = 312

2 × 3 × 5 × 11 = 330

2 × 13² = 338

2⁵ × 11 = 352

2 × 3 × 5 × 13 = 390

2⁵ × 13 = 416

3 × 11 × 13 = 429

2³ × 5 × 11 = 440

2⁵ × 3 × 5 = 480

3 × 13² = 507

2³ × 5 × 13 = 520

2⁴ × 3 × 11 = 528

2² × 11 × 13 = 572

2⁴ × 3 × 13 = 624

2² × 3 × 5 × 11 = 660

2² × 13² = 676

5 × 11 × 13 = 715

2² × 3 × 5 × 13 = 780

5 × 13² = 845

2 × 3 × 11 × 13 = 858

2⁴ × 5 × 11 = 880

This list continues below...

... This list continues from above

2 × 3 × 13² = 1,014

2⁴ × 5 × 13 = 1,040

2⁵ × 3 × 11 = 1,056

2³ × 11 × 13 = 1,144

2⁵ × 3 × 13 = 1,248

2³ × 3 × 5 × 11 = 1,320

2³ × 13² = 1,352

2 × 5 × 11 × 13 = 1,430

2³ × 3 × 5 × 13 = 1,560

2 × 5 × 13² = 1,690

2² × 3 × 11 × 13 = 1,716

2⁵ × 5 × 11 = 1,760

11 × 13² = 1,859

2² × 3 × 13² = 2,028

2⁵ × 5 × 13 = 2,080

3 × 5 × 11 × 13 = 2,145

2⁴ × 11 × 13 = 2,288

3 × 5 × 13² = 2,535

2⁴ × 3 × 5 × 11 = 2,640

2⁴ × 13² = 2,704

2² × 5 × 11 × 13 = 2,860

2⁴ × 3 × 5 × 13 = 3,120

2² × 5 × 13² = 3,380

2³ × 3 × 11 × 13 = 3,432

2 × 11 × 13² = 3,718

2³ × 3 × 13² = 4,056

2 × 3 × 5 × 11 × 13 = 4,290

2⁵ × 11 × 13 = 4,576

2 × 3 × 5 × 13² = 5,070

2⁵ × 3 × 5 × 11 = 5,280

2⁵ × 13² = 5,408

3 × 11 × 13² = 5,577

2³ × 5 × 11 × 13 = 5,720

2⁵ × 3 × 5 × 13 = 6,240

2³ × 5 × 13² = 6,760

2⁴ × 3 × 11 × 13 = 6,864

2² × 11 × 13² = 7,436

2⁴ × 3 × 13² = 8,112

2² × 3 × 5 × 11 × 13 = 8,580

5 × 11 × 13² = 9,295

2² × 3 × 5 × 13² = 10,140

2 × 3 × 11 × 13² = 11,154

2⁴ × 5 × 11 × 13 = 11,440

2⁴ × 5 × 13² = 13,520

2⁵ × 3 × 11 × 13 = 13,728

2³ × 11 × 13² = 14,872

2⁵ × 3 × 13² = 16,224

2³ × 3 × 5 × 11 × 13 = 17,160

2 × 5 × 11 × 13² = 18,590

2³ × 3 × 5 × 13² = 20,280

2² × 3 × 11 × 13² = 22,308

2⁵ × 5 × 11 × 13 = 22,880

2⁵ × 5 × 13² = 27,040

3 × 5 × 11 × 13² = 27,885

2⁴ × 11 × 13² = 29,744

2⁴ × 3 × 5 × 11 × 13 = 34,320

2² × 5 × 11 × 13² = 37,180

2⁴ × 3 × 5 × 13² = 40,560

2³ × 3 × 11 × 13² = 44,616

2 × 3 × 5 × 11 × 13² = 55,770

2⁵ × 11 × 13² = 59,488

2⁵ × 3 × 5 × 11 × 13 = 68,640

2³ × 5 × 11 × 13² = 74,360

2⁵ × 3 × 5 × 13² = 81,120

2⁴ × 3 × 11 × 13² = 89,232

2² × 3 × 5 × 11 × 13² = 111,540

2⁴ × 5 × 11 × 13² = 148,720

2⁵ × 3 × 11 × 13² = 178,464

2³ × 3 × 5 × 11 × 13² = 223,080

2⁵ × 5 × 11 × 13² = 297,440

2⁴ × 3 × 5 × 11 × 13² = 446,160

2⁵ × 3 × 5 × 11 × 13² = 892,320

The final answer:
(scroll down)

892,320 has 144 factors (divisors):
1; 2; 3; 4; 5; 6; 8; 10; 11; 12; 13; 15; 16; 20; 22; 24; 26; 30; 32; 33; 39; 40; 44; 48; 52; 55; 60; 65; 66; 78; 80; 88; 96; 104; 110; 120; 130; 132; 143; 156; 160; 165; 169; 176; 195; 208; 220; 240; 260; 264; 286; 312; 330; 338; 352; 390; 416; 429; 440; 480; 507; 520; 528; 572; 624; 660; 676; 715; 780; 845; 858; 880; 1,014; 1,040; 1,056; 1,144; 1,248; 1,320; 1,352; 1,430; 1,560; 1,690; 1,716; 1,760; 1,859; 2,028; 2,080; 2,145; 2,288; 2,535; 2,640; 2,704; 2,860; 3,120; 3,380; 3,432; 3,718; 4,056; 4,290; 4,576; 5,070; 5,280; 5,408; 5,577; 5,720; 6,240; 6,760; 6,864; 7,436; 8,112; 8,580; 9,295; 10,140; 11,154; 11,440; 13,520; 13,728; 14,872; 16,224; 17,160; 18,590; 20,280; 22,308; 22,880; 27,040; 27,885; 29,744; 34,320; 37,180; 40,560; 44,616; 55,770; 59,488; 68,640; 74,360; 81,120; 89,232; 111,540; 148,720; 178,464; 223,080; 297,440; 446,160 and 892,320
out of which 5 prime factors: 2; 3; 5; 11 and 13
892,320 and 1 are called by some authors improper factors (improper divisors), the others are called proper factors (proper divisors).

A quick way to find the factors (the divisors) of a number is to break it down into prime factors.

Then multiply the prime factors and their exponents, if any, in all their different combinations.

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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.

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The list of all the calculated factors (divisors) of one or two numbers

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".