What is the Greatest Common Factor of 61974 and 61984?

Greatest common factor (GCF) of 61974 and 61984 is 2.

GCF(61974,61984) = 2

We will now calculate the prime factors of 61974 and 61984, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 61974 and 61984.

How to find the GCF of 61974 and 61984?

We will first find the prime factorization of 61974 and 61984. After we will calculate the factors of 61974 and 61984 and find the biggest common factor number .

Step-1: Prime Factorization of 61974

Prime factors of 61974 are 2, 3, 11, 313. Prime factorization of 61974 in exponential form is:

61974 = 2¹ × 3² × 11¹ × 313¹

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 61974

List of positive integer factors of 61974 that divides 61974 without a remainder.

1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 198, 313, 626, 939, 1878, 2817, 3443, 5634, 6886, 10329, 20658, 30987

Step-4: Factors of 61984

List of positive integer factors of 61984 that divides 61974 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 61974 and 61984. The biggest common factor number is the GCF number.
So the greatest common factor 61974 and 61984 is 2.

Also check out the Least Common Multiple of 61974 and 61984