What is the Greatest Common Factor of 65940 and 65952?

Greatest common factor (GCF) of 65940 and 65952 is 12.

GCF(65940,65952) = 12

We will now calculate the prime factors of 65940 and 65952, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 65940 and 65952.

How to find the GCF of 65940 and 65952?

We will first find the prime factorization of 65940 and 65952. After we will calculate the factors of 65940 and 65952 and find the biggest common factor number .

Step-1: Prime Factorization of 65940

Prime factors of 65940 are 2, 3, 5, 7, 157. Prime factorization of 65940 in exponential form is:

65940 = 2² × 3¹ × 5¹ × 7¹ × 157¹

Step-2: Prime Factorization of 65952

Prime factors of 65952 are 2, 3, 229. Prime factorization of 65952 in exponential form is:

65952 = 2⁵ × 3² × 229¹

Step-3: Factors of 65940

List of positive integer factors of 65940 that divides 65940 without a remainder.

1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 157, 210, 314, 420, 471, 628, 785, 942, 1099, 1570, 1884, 2198, 2355, 3140, 3297, 4396, 4710, 5495, 6594, 9420, 10990, 13188, 16485, 21980, 32970

Step-4: Factors of 65952

List of positive integer factors of 65952 that divides 65940 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 229, 288, 458, 687, 916, 1374, 1832, 2061, 2748, 3664, 4122, 5496, 7328, 8244, 10992, 16488, 21984, 32976

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 65940 and 65952. The biggest common factor number is the GCF number.
So the greatest common factor 65940 and 65952 is 12.

Also check out the Least Common Multiple of 65940 and 65952