What is the Greatest Common Factor of 81954 and 81972?

Greatest common factor (GCF) of 81954 and 81972 is 18.

GCF(81954,81972) = 18

We will now calculate the prime factors of 81954 and 81972, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 81954 and 81972.

How to find the GCF of 81954 and 81972?

We will first find the prime factorization of 81954 and 81972. After we will calculate the factors of 81954 and 81972 and find the biggest common factor number .

Step-1: Prime Factorization of 81954

Prime factors of 81954 are 2, 3, 29, 157. Prime factorization of 81954 in exponential form is:

81954 = 2¹ × 3² × 29¹ × 157¹

Step-2: Prime Factorization of 81972

Prime factors of 81972 are 2, 3, 11, 23. Prime factorization of 81972 in exponential form is:

81972 = 2² × 3⁴ × 11¹ × 23¹

Step-3: Factors of 81954

List of positive integer factors of 81954 that divides 81954 without a remainder.

1, 2, 3, 6, 9, 18, 29, 58, 87, 157, 174, 261, 314, 471, 522, 942, 1413, 2826, 4553, 9106, 13659, 27318, 40977

Step-4: Factors of 81972

List of positive integer factors of 81972 that divides 81954 without a remainder.

1, 2, 3, 4, 6, 9, 11, 12, 18, 22, 23, 27, 33, 36, 44, 46, 54, 66, 69, 81, 92, 99, 108, 132, 138, 162, 198, 207, 253, 276, 297, 324, 396, 414, 506, 594, 621, 759, 828, 891, 1012, 1188, 1242, 1518, 1782, 1863, 2277, 2484, 3036, 3564, 3726, 4554, 6831, 7452, 9108, 13662, 20493, 27324, 40986

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 81954 and 81972. The biggest common factor number is the GCF number.
So the greatest common factor 81954 and 81972 is 18.

Also check out the Least Common Multiple of 81954 and 81972