What is the Greatest Common Factor of 1972 and 1986?

Greatest common factor (GCF) of 1972 and 1986 is 2.

GCF(1972,1986) = 2

We will now calculate the prime factors of 1972 and 1986, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1972 and 1986.

How to find the GCF of 1972 and 1986?

We will first find the prime factorization of 1972 and 1986. After we will calculate the factors of 1972 and 1986 and find the biggest common factor number .

Step-1: Prime Factorization of 1972

Prime factors of 1972 are 2, 17, 29. Prime factorization of 1972 in exponential form is:

1972 = 2² × 17¹ × 29¹

Step-2: Prime Factorization of 1986

Prime factors of 1986 are 2, 3, 331. Prime factorization of 1986 in exponential form is:

1986 = 2¹ × 3¹ × 331¹

Step-3: Factors of 1972

List of positive integer factors of 1972 that divides 1972 without a remainder.

1, 2, 4, 17, 29, 34, 58, 68, 116, 493, 986

Step-4: Factors of 1986

List of positive integer factors of 1986 that divides 1972 without a remainder.

1, 2, 3, 6, 331, 662, 993

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1972 and 1986. The biggest common factor number is the GCF number.
So the greatest common factor 1972 and 1986 is 2.

Also check out the Least Common Multiple of 1972 and 1986