What is the Greatest Common Factor of 81952 and 81972?

Greatest common factor (GCF) of 81952 and 81972 is 4.

GCF(81952,81972) = 4

We will now calculate the prime factors of 81952 and 81972, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 81952 and 81972.

How to find the GCF of 81952 and 81972?

We will first find the prime factorization of 81952 and 81972. After we will calculate the factors of 81952 and 81972 and find the biggest common factor number .

Step-1: Prime Factorization of 81952

Prime factors of 81952 are 2, 13, 197. Prime factorization of 81952 in exponential form is:

81952 = 2⁵ × 13¹ × 197¹

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 81952

List of positive integer factors of 81952 that divides 81952 without a remainder.

1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 197, 208, 394, 416, 788, 1576, 2561, 3152, 5122, 6304, 10244, 20488, 40976

Step-4: Factors of 81972

List of positive integer factors of 81972 that divides 81952 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 81952 and 81972. The biggest common factor number is the GCF number.
So the greatest common factor 81952 and 81972 is 4.

Also check out the Least Common Multiple of 81952 and 81972