What is the Greatest Common Factor of 47974 and 47978?

Greatest common factor (GCF) of 47974 and 47978 is 2.

GCF(47974,47978) = 2

We will now calculate the prime factors of 47974 and 47978, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 47974 and 47978.

How to find the GCF of 47974 and 47978?

We will first find the prime factorization of 47974 and 47978. After we will calculate the factors of 47974 and 47978 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 47978

Prime factors of 47978 are 2, 7, 23, 149. Prime factorization of 47978 in exponential form is:

47978 = 2¹ × 7¹ × 23¹ × 149¹

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 47978

List of positive integer factors of 47978 that divides 47974 without a remainder.

1, 2, 7, 14, 23, 46, 149, 161, 298, 322, 1043, 2086, 3427, 6854, 23989

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 47974 and 47978. The biggest common factor number is the GCF number.
So the greatest common factor 47974 and 47978 is 2.

Also check out the Least Common Multiple of 47974 and 47978