1,577,856 and 3,831,936: Calculate all the common factors (divisors) of the two numbers (and the prime factors)

The common factors (divisors) of the numbers 1,577,856 and 3,831,936

The common factors (divisors) of the numbers 1,577,856 and 3,831,936 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). Follow the two steps below.

The prime factorization of numbers:

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


1,577,856 = 27 × 3 × 7 × 587
1,577,856 is not a prime number but a composite one.


3,831,936 = 27 × 3 × 17 × 587
3,831,936 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.




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

Multiply all the common prime factors, taken by their smallest exponents (powers).


gcf, hcf, gcd (1,577,856; 3,831,936) = 27 × 3 × 587 = 225,408




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

225,408 = 27 × 3 × 587


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
23 = 8
22 × 3 = 12
24 = 16
23 × 3 = 24
25 = 32
24 × 3 = 48
26 = 64
This list continues below...
... This list continues from above
25 × 3 = 96
27 = 128
26 × 3 = 192
27 × 3 = 384
prime factor = 587
2 × 587 = 1,174
3 × 587 = 1,761
22 × 587 = 2,348
2 × 3 × 587 = 3,522
23 × 587 = 4,696
22 × 3 × 587 = 7,044
24 × 587 = 9,392
23 × 3 × 587 = 14,088
25 × 587 = 18,784
24 × 3 × 587 = 28,176
26 × 587 = 37,568
25 × 3 × 587 = 56,352
27 × 587 = 75,136
26 × 3 × 587 = 112,704
27 × 3 × 587 = 225,408

The final answer:

1,577,856 and 3,831,936 have 32 common factors (divisors):
1; 2; 3; 4; 6; 8; 12; 16; 24; 32; 48; 64; 96; 128; 192; 384; 587; 1,174; 1,761; 2,348; 3,522; 4,696; 7,044; 9,392; 14,088; 18,784; 28,176; 37,568; 56,352; 75,136; 112,704 and 225,408
out of which 3 prime factors: 2; 3 and 587

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.



Other operations of this type:

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.

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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)


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