What is the Greatest Common Factor of 746 and 762?

Greatest common factor (GCF) of 746 and 762 is 2.

GCF(746,762) = 2

We will now calculate the prime factors of 746 and 762, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 746 and 762.

How to find the GCF of 746 and 762?

We will first find the prime factorization of 746 and 762. After we will calculate the factors of 746 and 762 and find the biggest common factor number .

Step-1: Prime Factorization of 746

Prime factors of 746 are 2, 373. Prime factorization of 746 in exponential form is:

746 = 2¹ × 373¹

Step-2: Prime Factorization of 762

Prime factors of 762 are 2, 3, 127. Prime factorization of 762 in exponential form is:

762 = 2¹ × 3¹ × 127¹

Step-3: Factors of 746

List of positive integer factors of 746 that divides 746 without a remainder.

1, 2, 373

Step-4: Factors of 762

List of positive integer factors of 762 that divides 746 without a remainder.

1, 2, 3, 6, 127, 254, 381

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 746 and 762. The biggest common factor number is the GCF number.
So the greatest common factor 746 and 762 is 2.

Also check out the Least Common Multiple of 746 and 762