What is the Greatest Common Factor of 29974 and 29984?

Greatest common factor (GCF) of 29974 and 29984 is 2.

GCF(29974,29984) = 2

We will now calculate the prime factors of 29974 and 29984, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29974 and 29984.

How to find the GCF of 29974 and 29984?

We will first find the prime factorization of 29974 and 29984. After we will calculate the factors of 29974 and 29984 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 29984

Prime factors of 29984 are 2, 937. Prime factorization of 29984 in exponential form is:

29984 = 2⁵ × 937¹

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 29984

List of positive integer factors of 29984 that divides 29974 without a remainder.

1, 2, 4, 8, 16, 32, 937, 1874, 3748, 7496, 14992

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29974 and 29984. The biggest common factor number is the GCF number.
So the greatest common factor 29974 and 29984 is 2.

Also check out the Least Common Multiple of 29974 and 29984