336,000 and 768,000: All the common factors (divisors) and prime factors of the integer numbers

The common factors of numbers 336,000 and 768,000

The common factors (divisors) of numbers 336,000 and 768,000 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. Follow the two steps below.

Integer numbers prime factorization:

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


336,000 = 27 × 3 × 53 × 7;
336,000 is not a prime, is a composite number;


768,000 = 211 × 3 × 53;
768,000 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.




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

Multiply all the common prime factors, by the lowest exponents (if any).


Greatest (highest) common factor (divisor):


gcf, hcf, gcd (336,000; 768,000) = 27 × 3 × 53 = 48,000;




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

48,000 = 27 × 3 × 53


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
prime factor = 3
22 = 4
prime factor = 5
2 × 3 = 6
23 = 8
2 × 5 = 10
22 × 3 = 12
3 × 5 = 15
24 = 16
22 × 5 = 20
continued below...
... continued from above
23 × 3 = 24
52 = 25
2 × 3 × 5 = 30
25 = 32
23 × 5 = 40
24 × 3 = 48
2 × 52 = 50
22 × 3 × 5 = 60
26 = 64
3 × 52 = 75
24 × 5 = 80
25 × 3 = 96
22 × 52 = 100
23 × 3 × 5 = 120
53 = 125
27 = 128
2 × 3 × 52 = 150
25 × 5 = 160
26 × 3 = 192
23 × 52 = 200
24 × 3 × 5 = 240
2 × 53 = 250
22 × 3 × 52 = 300
26 × 5 = 320
3 × 53 = 375
27 × 3 = 384
24 × 52 = 400
25 × 3 × 5 = 480
22 × 53 = 500
23 × 3 × 52 = 600
27 × 5 = 640
2 × 3 × 53 = 750
25 × 52 = 800
26 × 3 × 5 = 960
23 × 53 = 1,000
24 × 3 × 52 = 1,200
22 × 3 × 53 = 1,500
26 × 52 = 1,600
27 × 3 × 5 = 1,920
24 × 53 = 2,000
25 × 3 × 52 = 2,400
23 × 3 × 53 = 3,000
27 × 52 = 3,200
25 × 53 = 4,000
26 × 3 × 52 = 4,800
24 × 3 × 53 = 6,000
26 × 53 = 8,000
27 × 3 × 52 = 9,600
25 × 3 × 53 = 12,000
27 × 53 = 16,000
26 × 3 × 53 = 24,000
27 × 3 × 53 = 48,000

Final answer:

336,000 and 768,000 have 64 common factors (divisors):
1; 2; 3; 4; 5; 6; 8; 10; 12; 15; 16; 20; 24; 25; 30; 32; 40; 48; 50; 60; 64; 75; 80; 96; 100; 120; 125; 128; 150; 160; 192; 200; 240; 250; 300; 320; 375; 384; 400; 480; 500; 600; 640; 750; 800; 960; 1,000; 1,200; 1,500; 1,600; 1,920; 2,000; 2,400; 3,000; 3,200; 4,000; 4,800; 6,000; 8,000; 9,600; 12,000; 16,000; 24,000 and 48,000
out of which 3 prime factors: 2; 3 and 5

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

Latest calculated factors (divisors)

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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