What is the Greatest Common Factor of 39825 and 39840?

Greatest common factor (GCF) of 39825 and 39840 is 15.

GCF(39825,39840) = 15

We will now calculate the prime factors of 39825 and 39840, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39825 and 39840.

How to find the GCF of 39825 and 39840?

We will first find the prime factorization of 39825 and 39840. After we will calculate the factors of 39825 and 39840 and find the biggest common factor number .

Step-1: Prime Factorization of 39825

Prime factors of 39825 are 3, 5, 59. Prime factorization of 39825 in exponential form is:

39825 = 3³ × 5² × 59¹

Step-2: Prime Factorization of 39840

Prime factors of 39840 are 2, 3, 5, 83. Prime factorization of 39840 in exponential form is:

39840 = 2⁵ × 3¹ × 5¹ × 83¹

Step-3: Factors of 39825

List of positive integer factors of 39825 that divides 39825 without a remainder.

1, 3, 5, 9, 15, 25, 27, 45, 59, 75, 135, 177, 225, 295, 531, 675, 885, 1475, 1593, 2655, 4425, 7965, 13275

Step-4: Factors of 39840

List of positive integer factors of 39840 that divides 39825 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 80, 83, 96, 120, 160, 166, 240, 249, 332, 415, 480, 498, 664, 830, 996, 1245, 1328, 1660, 1992, 2490, 2656, 3320, 3984, 4980, 6640, 7968, 9960, 13280, 19920

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39825 and 39840. The biggest common factor number is the GCF number.
So the greatest common factor 39825 and 39840 is 15.

Also check out the Least Common Multiple of 39825 and 39840