What is the Greatest Common Factor of 65952 and 65964?

Greatest common factor (GCF) of 65952 and 65964 is 12.

GCF(65952,65964) = 12

We will now calculate the prime factors of 65952 and 65964, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 65952 and 65964.

How to find the GCF of 65952 and 65964?

We will first find the prime factorization of 65952 and 65964. After we will calculate the factors of 65952 and 65964 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 65964

Prime factors of 65964 are 2, 3, 23, 239. Prime factorization of 65964 in exponential form is:

65964 = 2² × 3¹ × 23¹ × 239¹

Step-3: Factors of 65952

List of positive integer factors of 65952 that divides 65952 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

Step-4: Factors of 65964

List of positive integer factors of 65964 that divides 65952 without a remainder.

1, 2, 3, 4, 6, 12, 23, 46, 69, 92, 138, 239, 276, 478, 717, 956, 1434, 2868, 5497, 10994, 16491, 21988, 32982

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 65952 and 65964. The biggest common factor number is the GCF number.
So the greatest common factor 65952 and 65964 is 12.

Also check out the Least Common Multiple of 65952 and 65964