What is the Greatest Common Factor of 39480 and 39500?

Greatest common factor (GCF) of 39480 and 39500 is 20.

GCF(39480,39500) = 20

We will now calculate the prime factors of 39480 and 39500, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39480 and 39500.

How to find the GCF of 39480 and 39500?

We will first find the prime factorization of 39480 and 39500. After we will calculate the factors of 39480 and 39500 and find the biggest common factor number .

Step-1: Prime Factorization of 39480

Prime factors of 39480 are 2, 3, 5, 7, 47. Prime factorization of 39480 in exponential form is:

39480 = 2³ × 3¹ × 5¹ × 7¹ × 47¹

Step-2: Prime Factorization of 39500

Prime factors of 39500 are 2, 5, 79. Prime factorization of 39500 in exponential form is:

39500 = 2² × 5³ × 79¹

Step-3: Factors of 39480

List of positive integer factors of 39480 that divides 39480 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 47, 56, 60, 70, 84, 94, 105, 120, 140, 141, 168, 188, 210, 235, 280, 282, 329, 376, 420, 470, 564, 658, 705, 840, 940, 987, 1128, 1316, 1410, 1645, 1880, 1974, 2632, 2820, 3290, 3948, 4935, 5640, 6580, 7896, 9870, 13160, 19740

Step-4: Factors of 39500

List of positive integer factors of 39500 that divides 39480 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 79, 100, 125, 158, 250, 316, 395, 500, 790, 1580, 1975, 3950, 7900, 9875, 19750

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39480 and 39500. The biggest common factor number is the GCF number.
So the greatest common factor 39480 and 39500 is 20.

Also check out the Least Common Multiple of 39480 and 39500