What is the Greatest Common Factor of 69965 and 69972?

Greatest common factor (GCF) of 69965 and 69972 is 7.

GCF(69965,69972) = 7

We will now calculate the prime factors of 69965 and 69972, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 69965 and 69972.

How to find the GCF of 69965 and 69972?

We will first find the prime factorization of 69965 and 69972. After we will calculate the factors of 69965 and 69972 and find the biggest common factor number .

Step-1: Prime Factorization of 69965

Prime factors of 69965 are 5, 7, 1999. Prime factorization of 69965 in exponential form is:

69965 = 5¹ × 7¹ × 1999¹

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 69965

List of positive integer factors of 69965 that divides 69965 without a remainder.

1, 5, 7, 35, 1999, 9995, 13993

Step-4: Factors of 69972

List of positive integer factors of 69972 that divides 69965 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 69965 and 69972. The biggest common factor number is the GCF number.
So the greatest common factor 69965 and 69972 is 7.

Also check out the Least Common Multiple of 69965 and 69972