What is the Greatest Common Factor of 51748 and 51765?

Greatest common factor (GCF) of 51748 and 51765 is 17.

GCF(51748,51765) = 17

We will now calculate the prime factors of 51748 and 51765, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 51748 and 51765.

How to find the GCF of 51748 and 51765?

We will first find the prime factorization of 51748 and 51765. After we will calculate the factors of 51748 and 51765 and find the biggest common factor number .

Step-1: Prime Factorization of 51748

Prime factors of 51748 are 2, 17, 761. Prime factorization of 51748 in exponential form is:

51748 = 2² × 17¹ × 761¹

Step-2: Prime Factorization of 51765

Prime factors of 51765 are 3, 5, 7, 17, 29. Prime factorization of 51765 in exponential form is:

51765 = 3¹ × 5¹ × 7¹ × 17¹ × 29¹

Step-3: Factors of 51748

List of positive integer factors of 51748 that divides 51748 without a remainder.

1, 2, 4, 17, 34, 68, 761, 1522, 3044, 12937, 25874

Step-4: Factors of 51765

List of positive integer factors of 51765 that divides 51748 without a remainder.

1, 3, 5, 7, 15, 17, 21, 29, 35, 51, 85, 87, 105, 119, 145, 203, 255, 357, 435, 493, 595, 609, 1015, 1479, 1785, 2465, 3045, 3451, 7395, 10353, 17255

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 51748 and 51765. The biggest common factor number is the GCF number.
So the greatest common factor 51748 and 51765 is 17.

Also check out the Least Common Multiple of 51748 and 51765