What is the Greatest Common Factor of 69975 and 69984?

Greatest common factor (GCF) of 69975 and 69984 is 9.

GCF(69975,69984) = 9

We will now calculate the prime factors of 69975 and 69984, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 69975 and 69984.

How to find the GCF of 69975 and 69984?

We will first find the prime factorization of 69975 and 69984. After we will calculate the factors of 69975 and 69984 and find the biggest common factor number .

Step-1: Prime Factorization of 69975

Prime factors of 69975 are 3, 5, 311. Prime factorization of 69975 in exponential form is:

69975 = 3² × 5² × 311¹

Step-2: Prime Factorization of 69984

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

69984 = 2⁵ × 3⁷

Step-3: Factors of 69975

List of positive integer factors of 69975 that divides 69975 without a remainder.

1, 3, 5, 9, 15, 25, 45, 75, 225, 311, 933, 1555, 2799, 4665, 7775, 13995, 23325

Step-4: Factors of 69984

List of positive integer factors of 69984 that divides 69975 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 69975 and 69984. The biggest common factor number is the GCF number.
So the greatest common factor 69975 and 69984 is 9.

Also check out the Least Common Multiple of 69975 and 69984