What is the Greatest Common Factor of 69952 and 69972?

Greatest common factor (GCF) of 69952 and 69972 is 4.

GCF(69952,69972) = 4

We will now calculate the prime factors of 69952 and 69972, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 69952 and 69972.

How to find the GCF of 69952 and 69972?

We will first find the prime factorization of 69952 and 69972. After we will calculate the factors of 69952 and 69972 and find the biggest common factor number .

Step-1: Prime Factorization of 69952

Prime factors of 69952 are 2, 1093. Prime factorization of 69952 in exponential form is:

69952 = 2⁶ × 1093¹

Step-2: Prime Factorization of 69972

Prime factors of 69972 are 2, 3, 7, 17. Prime factorization of 69972 in exponential form is:

69972 = 2² × 3¹ × 7³ × 17¹

Step-3: Factors of 69952

List of positive integer factors of 69952 that divides 69952 without a remainder.

1, 2, 4, 8, 16, 32, 64, 1093, 2186, 4372, 8744, 17488, 34976

Step-4: Factors of 69972

List of positive integer factors of 69972 that divides 69952 without a remainder.

1, 2, 3, 4, 6, 7, 12, 14, 17, 21, 28, 34, 42, 49, 51, 68, 84, 98, 102, 119, 147, 196, 204, 238, 294, 343, 357, 476, 588, 686, 714, 833, 1029, 1372, 1428, 1666, 2058, 2499, 3332, 4116, 4998, 5831, 9996, 11662, 17493, 23324, 34986

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 69952 and 69972. The biggest common factor number is the GCF number.
So the greatest common factor 69952 and 69972 is 4.

Also check out the Least Common Multiple of 69952 and 69972