What is the Greatest Common Factor of 69984 and 69996?

Greatest common factor (GCF) of 69984 and 69996 is 12.

GCF(69984,69996) = 12

We will now calculate the prime factors of 69984 and 69996, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 69984 and 69996.

How to find the GCF of 69984 and 69996?

We will first find the prime factorization of 69984 and 69996. After we will calculate the factors of 69984 and 69996 and find the biggest common factor number .

Step-1: Prime Factorization of 69984

Prime factors of 69984 are 2, 3. Prime factorization of 69984 in exponential form is:

69984 = 2⁵ × 3⁷

Step-2: Prime Factorization of 69996

Prime factors of 69996 are 2, 3, 19, 307. Prime factorization of 69996 in exponential form is:

69996 = 2² × 3¹ × 19¹ × 307¹

Step-3: Factors of 69984

List of positive integer factors of 69984 that divides 69984 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 81, 96, 108, 144, 162, 216, 243, 288, 324, 432, 486, 648, 729, 864, 972, 1296, 1458, 1944, 2187, 2592, 2916, 3888, 4374, 5832, 7776, 8748, 11664, 17496, 23328, 34992

Step-4: Factors of 69996

List of positive integer factors of 69996 that divides 69984 without a remainder.

1, 2, 3, 4, 6, 12, 19, 38, 57, 76, 114, 228, 307, 614, 921, 1228, 1842, 3684, 5833, 11666, 17499, 23332, 34998

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 69984 and 69996. The biggest common factor number is the GCF number.
So the greatest common factor 69984 and 69996 is 12.

Also check out the Least Common Multiple of 69984 and 69996