What is the Greatest Common Factor of 5750 and 5762?

Greatest common factor (GCF) of 5750 and 5762 is 2.

GCF(5750,5762) = 2

We will now calculate the prime factors of 5750 and 5762, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5750 and 5762.

How to find the GCF of 5750 and 5762?

We will first find the prime factorization of 5750 and 5762. After we will calculate the factors of 5750 and 5762 and find the biggest common factor number .

Step-1: Prime Factorization of 5750

Prime factors of 5750 are 2, 5, 23. Prime factorization of 5750 in exponential form is:

5750 = 2¹ × 5³ × 23¹

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 5750

List of positive integer factors of 5750 that divides 5750 without a remainder.

1, 2, 5, 10, 23, 25, 46, 50, 115, 125, 230, 250, 575, 1150, 2875

Step-4: Factors of 5762

List of positive integer factors of 5762 that divides 5750 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5750 and 5762. The biggest common factor number is the GCF number.
So the greatest common factor 5750 and 5762 is 2.

Also check out the Least Common Multiple of 5750 and 5762