What is the Greatest Common Factor of 38500 and 38520?

Greatest common factor (GCF) of 38500 and 38520 is 20.

GCF(38500,38520) = 20

We will now calculate the prime factors of 38500 and 38520, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38500 and 38520.

How to find the GCF of 38500 and 38520?

We will first find the prime factorization of 38500 and 38520. After we will calculate the factors of 38500 and 38520 and find the biggest common factor number .

Step-1: Prime Factorization of 38500

Prime factors of 38500 are 2, 5, 7, 11. Prime factorization of 38500 in exponential form is:

38500 = 2² × 5³ × 7¹ × 11¹

Step-2: Prime Factorization of 38520

Prime factors of 38520 are 2, 3, 5, 107. Prime factorization of 38520 in exponential form is:

38520 = 2³ × 3² × 5¹ × 107¹

Step-3: Factors of 38500

List of positive integer factors of 38500 that divides 38500 without a remainder.

1, 2, 4, 5, 7, 10, 11, 14, 20, 22, 25, 28, 35, 44, 50, 55, 70, 77, 100, 110, 125, 140, 154, 175, 220, 250, 275, 308, 350, 385, 500, 550, 700, 770, 875, 1100, 1375, 1540, 1750, 1925, 2750, 3500, 3850, 5500, 7700, 9625, 19250

Step-4: Factors of 38520

List of positive integer factors of 38520 that divides 38500 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 107, 120, 180, 214, 321, 360, 428, 535, 642, 856, 963, 1070, 1284, 1605, 1926, 2140, 2568, 3210, 3852, 4280, 4815, 6420, 7704, 9630, 12840, 19260

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38500 and 38520. The biggest common factor number is the GCF number.
So the greatest common factor 38500 and 38520 is 20.

Also check out the Least Common Multiple of 38500 and 38520