What is the Greatest Common Factor of 61968 and 61984?

Greatest common factor (GCF) of 61968 and 61984 is 16.

GCF(61968,61984) = 16

We will now calculate the prime factors of 61968 and 61984, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 61968 and 61984.

How to find the GCF of 61968 and 61984?

We will first find the prime factorization of 61968 and 61984. After we will calculate the factors of 61968 and 61984 and find the biggest common factor number .

Step-1: Prime Factorization of 61968

Prime factors of 61968 are 2, 3, 1291. Prime factorization of 61968 in exponential form is:

61968 = 2⁴ × 3¹ × 1291¹

Step-2: Prime Factorization of 61984

Prime factors of 61984 are 2, 13, 149. Prime factorization of 61984 in exponential form is:

61984 = 2⁵ × 13¹ × 149¹

Step-3: Factors of 61968

List of positive integer factors of 61968 that divides 61968 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 1291, 2582, 3873, 5164, 7746, 10328, 15492, 20656, 30984

Step-4: Factors of 61984

List of positive integer factors of 61984 that divides 61968 without a remainder.

1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 149, 208, 298, 416, 596, 1192, 1937, 2384, 3874, 4768, 7748, 15496, 30992

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 61968 and 61984. The biggest common factor number is the GCF number.
So the greatest common factor 61968 and 61984 is 16.

Also check out the Least Common Multiple of 61968 and 61984