What is the Greatest Common Factor of 35972 and 35989?

Greatest common factor (GCF) of 35972 and 35989 is 17.

GCF(35972,35989) = 17

We will now calculate the prime factors of 35972 and 35989, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35972 and 35989.

How to find the GCF of 35972 and 35989?

We will first find the prime factorization of 35972 and 35989. After we will calculate the factors of 35972 and 35989 and find the biggest common factor number .

Step-1: Prime Factorization of 35972

Prime factors of 35972 are 2, 17, 23. Prime factorization of 35972 in exponential form is:

35972 = 2² × 17¹ × 23²

Step-2: Prime Factorization of 35989

Prime factors of 35989 are 17, 29, 73. Prime factorization of 35989 in exponential form is:

35989 = 17¹ × 29¹ × 73¹

Step-3: Factors of 35972

List of positive integer factors of 35972 that divides 35972 without a remainder.

1, 2, 4, 17, 23, 34, 46, 68, 92, 391, 529, 782, 1058, 1564, 2116, 8993, 17986

Step-4: Factors of 35989

List of positive integer factors of 35989 that divides 35972 without a remainder.

1, 17, 29, 73, 493, 1241, 2117

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35972 and 35989. The biggest common factor number is the GCF number.
So the greatest common factor 35972 and 35989 is 17.

Also check out the Least Common Multiple of 35972 and 35989