What is the Greatest Common Factor of 5746 and 5762?

Greatest common factor (GCF) of 5746 and 5762 is 2.

GCF(5746,5762) = 2

We will now calculate the prime factors of 5746 and 5762, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5746 and 5762.

How to find the GCF of 5746 and 5762?

We will first find the prime factorization of 5746 and 5762. After we will calculate the factors of 5746 and 5762 and find the biggest common factor number .

Step-1: Prime Factorization of 5746

Prime factors of 5746 are 2, 13, 17. Prime factorization of 5746 in exponential form is:

5746 = 2¹ × 13² × 17¹

Step-2: Prime Factorization of 5762

Prime factors of 5762 are 2, 43, 67. Prime factorization of 5762 in exponential form is:

5762 = 2¹ × 43¹ × 67¹

Step-3: Factors of 5746

List of positive integer factors of 5746 that divides 5746 without a remainder.

1, 2, 13, 17, 26, 34, 169, 221, 338, 442, 2873

Step-4: Factors of 5762

List of positive integer factors of 5762 that divides 5746 without a remainder.

1, 2, 43, 67, 86, 134, 2881

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5746 and 5762. The biggest common factor number is the GCF number.
So the greatest common factor 5746 and 5762 is 2.

Also check out the Least Common Multiple of 5746 and 5762