What is the Greatest Common Factor of 29974 and 29994?

Greatest common factor (GCF) of 29974 and 29994 is 2.

GCF(29974,29994) = 2

We will now calculate the prime factors of 29974 and 29994, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29974 and 29994.

How to find the GCF of 29974 and 29994?

We will first find the prime factorization of 29974 and 29994. After we will calculate the factors of 29974 and 29994 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 29994

Prime factors of 29994 are 2, 3, 4999. Prime factorization of 29994 in exponential form is:

29994 = 2¹ × 3¹ × 4999¹

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 29994

List of positive integer factors of 29994 that divides 29974 without a remainder.

1, 2, 3, 6, 4999, 9998, 14997

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29974 and 29994. The biggest common factor number is the GCF number.
So the greatest common factor 29974 and 29994 is 2.

Also check out the Least Common Multiple of 29974 and 29994