What is the Greatest Common Factor of 65744 and 65762?

Greatest common factor (GCF) of 65744 and 65762 is 2.

GCF(65744,65762) = 2

We will now calculate the prime factors of 65744 and 65762, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 65744 and 65762.

How to find the GCF of 65744 and 65762?

We will first find the prime factorization of 65744 and 65762. After we will calculate the factors of 65744 and 65762 and find the biggest common factor number .

Step-1: Prime Factorization of 65744

Prime factors of 65744 are 2, 7, 587. Prime factorization of 65744 in exponential form is:

65744 = 2⁴ × 7¹ × 587¹

Step-2: Prime Factorization of 65762

Prime factors of 65762 are 2, 131, 251. Prime factorization of 65762 in exponential form is:

65762 = 2¹ × 131¹ × 251¹

Step-3: Factors of 65744

List of positive integer factors of 65744 that divides 65744 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 56, 112, 587, 1174, 2348, 4109, 4696, 8218, 9392, 16436, 32872

Step-4: Factors of 65762

List of positive integer factors of 65762 that divides 65744 without a remainder.

1, 2, 131, 251, 262, 502, 32881

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 65744 and 65762. The biggest common factor number is the GCF number.
So the greatest common factor 65744 and 65762 is 2.

Also check out the Least Common Multiple of 65744 and 65762