What is the Greatest Common Factor of 35748 and 35766?

Greatest common factor (GCF) of 35748 and 35766 is 18.

GCF(35748,35766) = 18

We will now calculate the prime factors of 35748 and 35766, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35748 and 35766.

How to find the GCF of 35748 and 35766?

We will first find the prime factorization of 35748 and 35766. After we will calculate the factors of 35748 and 35766 and find the biggest common factor number .

Step-1: Prime Factorization of 35748

Prime factors of 35748 are 2, 3, 331. Prime factorization of 35748 in exponential form is:

35748 = 2² × 3³ × 331¹

Step-2: Prime Factorization of 35766

Prime factors of 35766 are 2, 3, 1987. Prime factorization of 35766 in exponential form is:

35766 = 2¹ × 3² × 1987¹

Step-3: Factors of 35748

List of positive integer factors of 35748 that divides 35748 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108, 331, 662, 993, 1324, 1986, 2979, 3972, 5958, 8937, 11916, 17874

Step-4: Factors of 35766

List of positive integer factors of 35766 that divides 35748 without a remainder.

1, 2, 3, 6, 9, 18, 1987, 3974, 5961, 11922, 17883

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35748 and 35766. The biggest common factor number is the GCF number.
So the greatest common factor 35748 and 35766 is 18.

Also check out the Least Common Multiple of 35748 and 35766