What is the Greatest Common Factor of 47974 and 47984?

Greatest common factor (GCF) of 47974 and 47984 is 2.

GCF(47974,47984) = 2

We will now calculate the prime factors of 47974 and 47984, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 47974 and 47984.

How to find the GCF of 47974 and 47984?

We will first find the prime factorization of 47974 and 47984. After we will calculate the factors of 47974 and 47984 and find the biggest common factor number .

Step-1: Prime Factorization of 47974

Prime factors of 47974 are 2, 17, 83. Prime factorization of 47974 in exponential form is:

47974 = 2¹ × 17² × 83¹

Step-2: Prime Factorization of 47984

Prime factors of 47984 are 2, 2999. Prime factorization of 47984 in exponential form is:

47984 = 2⁴ × 2999¹

Step-3: Factors of 47974

List of positive integer factors of 47974 that divides 47974 without a remainder.

1, 2, 17, 34, 83, 166, 289, 578, 1411, 2822, 23987

Step-4: Factors of 47984

List of positive integer factors of 47984 that divides 47974 without a remainder.

1, 2, 4, 8, 16, 2999, 5998, 11996, 23992

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 47974 and 47984. The biggest common factor number is the GCF number.
So the greatest common factor 47974 and 47984 is 2.

Also check out the Least Common Multiple of 47974 and 47984