What is the Greatest Common Factor of 84960 and 84972?

Greatest common factor (GCF) of 84960 and 84972 is 12.

GCF(84960,84972) = 12

We will now calculate the prime factors of 84960 and 84972, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 84960 and 84972.

How to find the GCF of 84960 and 84972?

We will first find the prime factorization of 84960 and 84972. After we will calculate the factors of 84960 and 84972 and find the biggest common factor number .

Step-1: Prime Factorization of 84960

Prime factors of 84960 are 2, 3, 5, 59. Prime factorization of 84960 in exponential form is:

84960 = 2⁵ × 3² × 5¹ × 59¹

Step-2: Prime Factorization of 84972

Prime factors of 84972 are 2, 3, 73, 97. Prime factorization of 84972 in exponential form is:

84972 = 2² × 3¹ × 73¹ × 97¹

Step-3: Factors of 84960

List of positive integer factors of 84960 that divides 84960 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 32, 36, 40, 45, 48, 59, 60, 72, 80, 90, 96, 118, 120, 144, 160, 177, 180, 236, 240, 288, 295, 354, 360, 472, 480, 531, 590, 708, 720, 885, 944, 1062, 1180, 1416, 1440, 1770, 1888, 2124, 2360, 2655, 2832, 3540, 4248, 4720, 5310, 5664, 7080, 8496, 9440, 10620, 14160, 16992, 21240, 28320, 42480

Step-4: Factors of 84972

List of positive integer factors of 84972 that divides 84960 without a remainder.

1, 2, 3, 4, 6, 12, 73, 97, 146, 194, 219, 291, 292, 388, 438, 582, 876, 1164, 7081, 14162, 21243, 28324, 42486

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 84960 and 84972. The biggest common factor number is the GCF number.
So the greatest common factor 84960 and 84972 is 12.

Also check out the Least Common Multiple of 84960 and 84972