What is the Greatest Common Factor of 35971 and 35984?

Greatest common factor (GCF) of 35971 and 35984 is 13.

GCF(35971,35984) = 13

We will now calculate the prime factors of 35971 and 35984, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35971 and 35984.

How to find the GCF of 35971 and 35984?

We will first find the prime factorization of 35971 and 35984. After we will calculate the factors of 35971 and 35984 and find the biggest common factor number .

Step-1: Prime Factorization of 35971

Prime factors of 35971 are 13, 2767. Prime factorization of 35971 in exponential form is:

35971 = 13¹ × 2767¹

Step-2: Prime Factorization of 35984

Prime factors of 35984 are 2, 13, 173. Prime factorization of 35984 in exponential form is:

35984 = 2⁴ × 13¹ × 173¹

Step-3: Factors of 35971

List of positive integer factors of 35971 that divides 35971 without a remainder.

1, 13, 2767

Step-4: Factors of 35984

List of positive integer factors of 35984 that divides 35971 without a remainder.

1, 2, 4, 8, 13, 16, 26, 52, 104, 173, 208, 346, 692, 1384, 2249, 2768, 4498, 8996, 17992

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35971 and 35984. The biggest common factor number is the GCF number.
So the greatest common factor 35971 and 35984 is 13.

Also check out the Least Common Multiple of 35971 and 35984