What is the Greatest Common Factor of 35974 and 35980?

Greatest common factor (GCF) of 35974 and 35980 is 2.

GCF(35974,35980) = 2

We will now calculate the prime factors of 35974 and 35980, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35974 and 35980.

How to find the GCF of 35974 and 35980?

We will first find the prime factorization of 35974 and 35980. After we will calculate the factors of 35974 and 35980 and find the biggest common factor number .

Step-1: Prime Factorization of 35974

Prime factors of 35974 are 2, 17987. Prime factorization of 35974 in exponential form is:

35974 = 2¹ × 17987¹

Step-2: Prime Factorization of 35980

Prime factors of 35980 are 2, 5, 7, 257. Prime factorization of 35980 in exponential form is:

35980 = 2² × 5¹ × 7¹ × 257¹

Step-3: Factors of 35974

List of positive integer factors of 35974 that divides 35974 without a remainder.

1, 2, 17987

Step-4: Factors of 35980

List of positive integer factors of 35980 that divides 35974 without a remainder.

1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140, 257, 514, 1028, 1285, 1799, 2570, 3598, 5140, 7196, 8995, 17990

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35974 and 35980. The biggest common factor number is the GCF number.
So the greatest common factor 35974 and 35980 is 2.

Also check out the Least Common Multiple of 35974 and 35980