What is the Greatest Common Factor of 71748 and 71766?

Greatest common factor (GCF) of 71748 and 71766 is 18.

GCF(71748,71766) = 18

We will now calculate the prime factors of 71748 and 71766, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 71748 and 71766.

How to find the GCF of 71748 and 71766?

We will first find the prime factorization of 71748 and 71766. After we will calculate the factors of 71748 and 71766 and find the biggest common factor number .

Step-1: Prime Factorization of 71748

Prime factors of 71748 are 2, 3, 1993. Prime factorization of 71748 in exponential form is:

71748 = 2² × 3² × 1993¹

Step-2: Prime Factorization of 71766

Prime factors of 71766 are 2, 3, 443. Prime factorization of 71766 in exponential form is:

71766 = 2¹ × 3⁴ × 443¹

Step-3: Factors of 71748

List of positive integer factors of 71748 that divides 71748 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 36, 1993, 3986, 5979, 7972, 11958, 17937, 23916, 35874

Step-4: Factors of 71766

List of positive integer factors of 71766 that divides 71748 without a remainder.

1, 2, 3, 6, 9, 18, 27, 54, 81, 162, 443, 886, 1329, 2658, 3987, 7974, 11961, 23922, 35883

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 71748 and 71766. The biggest common factor number is the GCF number.
So the greatest common factor 71748 and 71766 is 18.

Also check out the Least Common Multiple of 71748 and 71766