What is the Greatest Common Factor of 29974 and 29980?

Greatest common factor (GCF) of 29974 and 29980 is 2.

GCF(29974,29980) = 2

We will now calculate the prime factors of 29974 and 29980, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29974 and 29980.

How to find the GCF of 29974 and 29980?

We will first find the prime factorization of 29974 and 29980. After we will calculate the factors of 29974 and 29980 and find the biggest common factor number .

Step-1: Prime Factorization of 29974

Prime factors of 29974 are 2, 7, 2141. Prime factorization of 29974 in exponential form is:

29974 = 2¹ × 7¹ × 2141¹

Step-2: Prime Factorization of 29980

Prime factors of 29980 are 2, 5, 1499. Prime factorization of 29980 in exponential form is:

29980 = 2² × 5¹ × 1499¹

Step-3: Factors of 29974

List of positive integer factors of 29974 that divides 29974 without a remainder.

1, 2, 7, 14, 2141, 4282, 14987

Step-4: Factors of 29980

List of positive integer factors of 29980 that divides 29974 without a remainder.

1, 2, 4, 5, 10, 20, 1499, 2998, 5996, 7495, 14990

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29974 and 29980. The biggest common factor number is the GCF number.
So the greatest common factor 29974 and 29980 is 2.

Also check out the Least Common Multiple of 29974 and 29980