What is the Greatest Common Factor of 65730 and 65734?

Greatest common factor (GCF) of 65730 and 65734 is 2.

GCF(65730,65734) = 2

We will now calculate the prime factors of 65730 and 65734, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 65730 and 65734.

How to find the GCF of 65730 and 65734?

We will first find the prime factorization of 65730 and 65734. After we will calculate the factors of 65730 and 65734 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 65734

Prime factors of 65734 are 2, 23, 1429. Prime factorization of 65734 in exponential form is:

65734 = 2¹ × 23¹ × 1429¹

Step-3: Factors of 65730

List of positive integer factors of 65730 that divides 65730 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

Step-4: Factors of 65734

List of positive integer factors of 65734 that divides 65730 without a remainder.

1, 2, 23, 46, 1429, 2858, 32867

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 65730 and 65734. The biggest common factor number is the GCF number.
So the greatest common factor 65730 and 65734 is 2.

Also check out the Least Common Multiple of 65730 and 65734