What is the Greatest Common Factor of 54730 and 54750?

Greatest common factor (GCF) of 54730 and 54750 is 10.

GCF(54730,54750) = 10

We will now calculate the prime factors of 54730 and 54750, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 54730 and 54750.

How to find the GCF of 54730 and 54750?

We will first find the prime factorization of 54730 and 54750. After we will calculate the factors of 54730 and 54750 and find the biggest common factor number .

Step-1: Prime Factorization of 54730

Prime factors of 54730 are 2, 5, 13, 421. Prime factorization of 54730 in exponential form is:

54730 = 2¹ × 5¹ × 13¹ × 421¹

Step-2: Prime Factorization of 54750

Prime factors of 54750 are 2, 3, 5, 73. Prime factorization of 54750 in exponential form is:

54750 = 2¹ × 3¹ × 5³ × 73¹

Step-3: Factors of 54730

List of positive integer factors of 54730 that divides 54730 without a remainder.

1, 2, 5, 10, 13, 26, 65, 130, 421, 842, 2105, 4210, 5473, 10946, 27365

Step-4: Factors of 54750

List of positive integer factors of 54750 that divides 54730 without a remainder.

1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 73, 75, 125, 146, 150, 219, 250, 365, 375, 438, 730, 750, 1095, 1825, 2190, 3650, 5475, 9125, 10950, 18250, 27375

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 54730 and 54750. The biggest common factor number is the GCF number.
So the greatest common factor 54730 and 54750 is 10.

Also check out the Least Common Multiple of 54730 and 54750