What is the Greatest Common Factor of 34980 and 34992?

Greatest common factor (GCF) of 34980 and 34992 is 12.

GCF(34980,34992) = 12

We will now calculate the prime factors of 34980 and 34992, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34980 and 34992.

How to find the GCF of 34980 and 34992?

We will first find the prime factorization of 34980 and 34992. After we will calculate the factors of 34980 and 34992 and find the biggest common factor number .

Step-1: Prime Factorization of 34980

Prime factors of 34980 are 2, 3, 5, 11, 53. Prime factorization of 34980 in exponential form is:

34980 = 2² × 3¹ × 5¹ × 11¹ × 53¹

Step-2: Prime Factorization of 34992

Prime factors of 34992 are 2, 3. Prime factorization of 34992 in exponential form is:

34992 = 2⁴ × 3⁷

Step-3: Factors of 34980

List of positive integer factors of 34980 that divides 34980 without a remainder.

1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 30, 33, 44, 53, 55, 60, 66, 106, 110, 132, 159, 165, 212, 220, 265, 318, 330, 530, 583, 636, 660, 795, 1060, 1166, 1590, 1749, 2332, 2915, 3180, 3498, 5830, 6996, 8745, 11660, 17490

Step-4: Factors of 34992

List of positive integer factors of 34992 that divides 34980 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 81, 108, 144, 162, 216, 243, 324, 432, 486, 648, 729, 972, 1296, 1458, 1944, 2187, 2916, 3888, 4374, 5832, 8748, 11664, 17496

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34980 and 34992. The biggest common factor number is the GCF number.
So the greatest common factor 34980 and 34992 is 12.

Also check out the Least Common Multiple of 34980 and 34992