What is the Greatest Common Factor of 35500 and 35520?

Greatest common factor (GCF) of 35500 and 35520 is 20.

GCF(35500,35520) = 20

We will now calculate the prime factors of 35500 and 35520, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35500 and 35520.

How to find the GCF of 35500 and 35520?

We will first find the prime factorization of 35500 and 35520. After we will calculate the factors of 35500 and 35520 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 35520

Prime factors of 35520 are 2, 3, 5, 37. Prime factorization of 35520 in exponential form is:

35520 = 2⁶ × 3¹ × 5¹ × 37¹

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 35520

List of positive integer factors of 35520 that divides 35500 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 37, 40, 48, 60, 64, 74, 80, 96, 111, 120, 148, 160, 185, 192, 222, 240, 296, 320, 370, 444, 480, 555, 592, 740, 888, 960, 1110, 1184, 1480, 1776, 2220, 2368, 2960, 3552, 4440, 5920, 7104, 8880, 11840, 17760

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35500 and 35520. The biggest common factor number is the GCF number.
So the greatest common factor 35500 and 35520 is 20.

Also check out the Least Common Multiple of 35500 and 35520