What is the Greatest Common Factor of 6954 and 6972?

Greatest common factor (GCF) of 6954 and 6972 is 6.

GCF(6954,6972) = 6

We will now calculate the prime factors of 6954 and 6972, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 6954 and 6972.

How to find the GCF of 6954 and 6972?

We will first find the prime factorization of 6954 and 6972. After we will calculate the factors of 6954 and 6972 and find the biggest common factor number .

Step-1: Prime Factorization of 6954

Prime factors of 6954 are 2, 3, 19, 61. Prime factorization of 6954 in exponential form is:

6954 = 2¹ × 3¹ × 19¹ × 61¹

Step-2: Prime Factorization of 6972

Prime factors of 6972 are 2, 3, 7, 83. Prime factorization of 6972 in exponential form is:

6972 = 2² × 3¹ × 7¹ × 83¹

Step-3: Factors of 6954

List of positive integer factors of 6954 that divides 6954 without a remainder.

1, 2, 3, 6, 19, 38, 57, 61, 114, 122, 183, 366, 1159, 2318, 3477

Step-4: Factors of 6972

List of positive integer factors of 6972 that divides 6954 without a remainder.

1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 83, 84, 166, 249, 332, 498, 581, 996, 1162, 1743, 2324, 3486

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 6954 and 6972. The biggest common factor number is the GCF number.
So the greatest common factor 6954 and 6972 is 6.

Also check out the Least Common Multiple of 6954 and 6972