What is the Greatest Common Factor of 1748 and 1766?

Greatest common factor (GCF) of 1748 and 1766 is 2.

GCF(1748,1766) = 2

We will now calculate the prime factors of 1748 and 1766, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1748 and 1766.

How to find the GCF of 1748 and 1766?

We will first find the prime factorization of 1748 and 1766. After we will calculate the factors of 1748 and 1766 and find the biggest common factor number .

Step-1: Prime Factorization of 1748

Prime factors of 1748 are 2, 19, 23. Prime factorization of 1748 in exponential form is:

1748 = 2² × 19¹ × 23¹

Step-2: Prime Factorization of 1766

Prime factors of 1766 are 2, 883. Prime factorization of 1766 in exponential form is:

1766 = 2¹ × 883¹

Step-3: Factors of 1748

List of positive integer factors of 1748 that divides 1748 without a remainder.

1, 2, 4, 19, 23, 38, 46, 76, 92, 437, 874

Step-4: Factors of 1766

List of positive integer factors of 1766 that divides 1748 without a remainder.

1, 2, 883

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1748 and 1766. The biggest common factor number is the GCF number.
So the greatest common factor 1748 and 1766 is 2.

Also check out the Least Common Multiple of 1748 and 1766