What is the Greatest Common Factor of 65724 and 65730?

Greatest common factor (GCF) of 65724 and 65730 is 6.

GCF(65724,65730) = 6

We will now calculate the prime factors of 65724 and 65730, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 65724 and 65730.

How to find the GCF of 65724 and 65730?

We will first find the prime factorization of 65724 and 65730. After we will calculate the factors of 65724 and 65730 and find the biggest common factor number .

Step-1: Prime Factorization of 65724

Prime factors of 65724 are 2, 3, 5477. Prime factorization of 65724 in exponential form is:

65724 = 2² × 3¹ × 5477¹

Step-2: Prime Factorization of 65730

Prime factors of 65730 are 2, 3, 5, 7, 313. Prime factorization of 65730 in exponential form is:

65730 = 2¹ × 3¹ × 5¹ × 7¹ × 313¹

Step-3: Factors of 65724

List of positive integer factors of 65724 that divides 65724 without a remainder.

1, 2, 3, 4, 6, 12, 5477, 10954, 16431, 21908, 32862

Step-4: Factors of 65730

List of positive integer factors of 65730 that divides 65724 without a remainder.

1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210, 313, 626, 939, 1565, 1878, 2191, 3130, 4382, 4695, 6573, 9390, 10955, 13146, 21910, 32865

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 65724 and 65730. The biggest common factor number is the GCF number.
So the greatest common factor 65724 and 65730 is 6.

Also check out the Least Common Multiple of 65724 and 65730