436,744 and 873,488: All the common factors (divisors) and prime factors of the integer numbers

The common factors of numbers 436,744 and 873,488

The common factors (divisors) of numbers 436,744 and 873,488 are all the factors (divisors) of their 'greatest (highest) common factor (divisor)'.

Note

Factor of a number A: a number B that when multiplied with another C produces the given number A. Both B and C are factors of A.



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

Divide the larger number by the smaller one.


Notice that dividing our numbers leaves no remainder:


873,488 ÷ 436,744 = 2 + 0;


=> 873,488 = 436,744 × 2;


So, 873,488 is divisible by 436,744;


436,744 is a factor (a divisor) of 873,488;


Consequently, greatest (highest) common factor (divisor):
gcf, hcf, gcd (436,744; 873,488) = 436,744;




Get the prime factorization of GCF (HCF, GCD)

Prime Factorization of a number: finding the prime numbers that multiply together to make that number.


436,744 = 23 × 7 × 11 × 709;
436,744 is not a prime, is a composite number.


* Positive integers that are only dividing by themselves and 1 are called prime numbers. A prime number has only two factors: 1 and itself.
* A composite number is a positive integer that has at least one factor (divisor) other than 1 and itself.




Find all the factors (divisors) of the GCF (HCF, GCD)

436,744 = 23 × 7 × 11 × 709


Get all the combinations (multiplications) of the prime factors of GFC (HCF, GCD) that give different results.


When combining the prime factors also consider their exponents.


Also add 1 to the list of factors (divisors). Any number is divisible by 1.


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



Factors (divisors) list:

neither a prime nor a composite = 1
prime factor = 2
22 = 4
prime factor = 7
23 = 8
prime factor = 11
2 × 7 = 14
2 × 11 = 22
22 × 7 = 28
22 × 11 = 44
23 × 7 = 56
7 × 11 = 77
continued below...
... continued from above
23 × 11 = 88
2 × 7 × 11 = 154
22 × 7 × 11 = 308
23 × 7 × 11 = 616
prime factor = 709
2 × 709 = 1,418
22 × 709 = 2,836
7 × 709 = 4,963
23 × 709 = 5,672
11 × 709 = 7,799
2 × 7 × 709 = 9,926
2 × 11 × 709 = 15,598
22 × 7 × 709 = 19,852
22 × 11 × 709 = 31,196
23 × 7 × 709 = 39,704
7 × 11 × 709 = 54,593
23 × 11 × 709 = 62,392
2 × 7 × 11 × 709 = 109,186
22 × 7 × 11 × 709 = 218,372
23 × 7 × 11 × 709 = 436,744

Final answer:

436,744 and 873,488 have 32 common factors (divisors):
1; 2; 4; 7; 8; 11; 14; 22; 28; 44; 56; 77; 88; 154; 308; 616; 709; 1,418; 2,836; 4,963; 5,672; 7,799; 9,926; 15,598; 19,852; 31,196; 39,704; 54,593; 62,392; 109,186; 218,372 and 436,744
out of which 4 prime factors: 2; 7; 11 and 709

The key to find the divisors of a number is to build its prime factorization.


Then determine all the different combinations (multiplications) of the prime factors, and their exponents, if any.



More operations of this kind:

Calculator: all the (common) factors (divisors) of numbers

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Tutoring: 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 "t" is a factor (divisor) of "a" then among the prime factors of "t" will appear only prime factors that also appear on the prime factorization of "a" and the maximum of their exponents (powers, or multiplicities) is at most equal to those involved in the prime factorization of "a".

For example, 12 is a factor (divisor) of 60:

  • 12 = 2 × 2 × 3 = 22 × 3
  • 60 = 2 × 2 × 3 × 5 = 22 × 3 × 5

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 both the prime factorizations of "a" and "b", by lower or at most by equal powers (exponents, or multiplicities).

For example, 12 is the common factor of 48 and 360. After running both numbers' prime factorizations (factoring them down to prime factors):

  • 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, is the product of all prime factors involved in both the prime factorizations of "a" and "b", by the lowest powers (multiplicities).

Based on this rule it is calculated the greatest common factor, GCF, (or greatest common divisor GCD, HCF) of several numbers, as shown in the example below:

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

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).

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".


What is a prime number?

What is a composite number?

Prime numbers up to 1,000

Prime numbers up to 10,000

Sieve of Eratosthenes

Euclid's algorithm

Simplifying ordinary (common) math fractions (reducing to lower terms): steps to follow and examples