123,225,144 and 0: Calculate all the common factors (divisors) of the two numbers (and the prime factors)

The common factors (divisors) of the numbers 123,225,144 and 0

The common factors (divisors) of the numbers 123,225,144 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 (123,225,144; 0) = 123,225,144


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




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.


123,225,144 = 23 × 3 × 7 × 113 × 6,491
123,225,144 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.




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

123,225,144 = 23 × 3 × 7 × 113 × 6,491


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
2 × 3 = 6
prime factor = 7
23 = 8
22 × 3 = 12
2 × 7 = 14
3 × 7 = 21
23 × 3 = 24
22 × 7 = 28
2 × 3 × 7 = 42
23 × 7 = 56
22 × 3 × 7 = 84
prime factor = 113
23 × 3 × 7 = 168
2 × 113 = 226
3 × 113 = 339
22 × 113 = 452
2 × 3 × 113 = 678
7 × 113 = 791
23 × 113 = 904
22 × 3 × 113 = 1,356
2 × 7 × 113 = 1,582
3 × 7 × 113 = 2,373
23 × 3 × 113 = 2,712
22 × 7 × 113 = 3,164
2 × 3 × 7 × 113 = 4,746
23 × 7 × 113 = 6,328
prime factor = 6,491
22 × 3 × 7 × 113 = 9,492
This list continues below...

... This list continues from above
2 × 6,491 = 12,982
23 × 3 × 7 × 113 = 18,984
3 × 6,491 = 19,473
22 × 6,491 = 25,964
2 × 3 × 6,491 = 38,946
7 × 6,491 = 45,437
23 × 6,491 = 51,928
22 × 3 × 6,491 = 77,892
2 × 7 × 6,491 = 90,874
3 × 7 × 6,491 = 136,311
23 × 3 × 6,491 = 155,784
22 × 7 × 6,491 = 181,748
2 × 3 × 7 × 6,491 = 272,622
23 × 7 × 6,491 = 363,496
22 × 3 × 7 × 6,491 = 545,244
113 × 6,491 = 733,483
23 × 3 × 7 × 6,491 = 1,090,488
2 × 113 × 6,491 = 1,466,966
3 × 113 × 6,491 = 2,200,449
22 × 113 × 6,491 = 2,933,932
2 × 3 × 113 × 6,491 = 4,400,898
7 × 113 × 6,491 = 5,134,381
23 × 113 × 6,491 = 5,867,864
22 × 3 × 113 × 6,491 = 8,801,796
2 × 7 × 113 × 6,491 = 10,268,762
3 × 7 × 113 × 6,491 = 15,403,143
23 × 3 × 113 × 6,491 = 17,603,592
22 × 7 × 113 × 6,491 = 20,537,524
2 × 3 × 7 × 113 × 6,491 = 30,806,286
23 × 7 × 113 × 6,491 = 41,075,048
22 × 3 × 7 × 113 × 6,491 = 61,612,572
23 × 3 × 7 × 113 × 6,491 = 123,225,144

The final answer:
(scroll down)

123,225,144 and 0 have 64 common factors (divisors):
1; 2; 3; 4; 6; 7; 8; 12; 14; 21; 24; 28; 42; 56; 84; 113; 168; 226; 339; 452; 678; 791; 904; 1,356; 1,582; 2,373; 2,712; 3,164; 4,746; 6,328; 6,491; 9,492; 12,982; 18,984; 19,473; 25,964; 38,946; 45,437; 51,928; 77,892; 90,874; 136,311; 155,784; 181,748; 272,622; 363,496; 545,244; 733,483; 1,090,488; 1,466,966; 2,200,449; 2,933,932; 4,400,898; 5,134,381; 5,867,864; 8,801,796; 10,268,762; 15,403,143; 17,603,592; 20,537,524; 30,806,286; 41,075,048; 61,612,572 and 123,225,144
out of which 5 prime factors: 2; 3; 7; 113 and 6,491

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

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)


What is a prime number? Definition, examples

What is a composite number? Definition, examples

The prime numbers up to 1,000

The prime numbers up to 10,000

The Sieve of Eratosthenes

The Euclidean Algorithm

Completely reduce (simplify) fractions to the lowest terms: Steps and Examples