What is the Greatest Common Factor of 35500 and 35514?

Greatest common factor (GCF) of 35500 and 35514 is 2.

GCF(35500,35514) = 2

We will now calculate the prime factors of 35500 and 35514, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35500 and 35514.

How to find the GCF of 35500 and 35514?

We will first find the prime factorization of 35500 and 35514. After we will calculate the factors of 35500 and 35514 and find the biggest common factor number .

Step-1: Prime Factorization of 35500

Prime factors of 35500 are 2, 5, 71. Prime factorization of 35500 in exponential form is:

35500 = 2² × 5³ × 71¹

Step-2: Prime Factorization of 35514

Prime factors of 35514 are 2, 3, 1973. Prime factorization of 35514 in exponential form is:

35514 = 2¹ × 3² × 1973¹

Step-3: Factors of 35500

List of positive integer factors of 35500 that divides 35500 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 71, 100, 125, 142, 250, 284, 355, 500, 710, 1420, 1775, 3550, 7100, 8875, 17750

Step-4: Factors of 35514

List of positive integer factors of 35514 that divides 35500 without a remainder.

1, 2, 3, 6, 9, 18, 1973, 3946, 5919, 11838, 17757

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35500 and 35514. The biggest common factor number is the GCF number.
So the greatest common factor 35500 and 35514 is 2.

Also check out the Least Common Multiple of 35500 and 35514