What is the Greatest Common Factor of 69825 and 69840?

Greatest common factor (GCF) of 69825 and 69840 is 15.

GCF(69825,69840) = 15

We will now calculate the prime factors of 69825 and 69840, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 69825 and 69840.

How to find the GCF of 69825 and 69840?

We will first find the prime factorization of 69825 and 69840. After we will calculate the factors of 69825 and 69840 and find the biggest common factor number .

Step-1: Prime Factorization of 69825

Prime factors of 69825 are 3, 5, 7, 19. Prime factorization of 69825 in exponential form is:

69825 = 3¹ × 5² × 7² × 19¹

Step-2: Prime Factorization of 69840

Prime factors of 69840 are 2, 3, 5, 97. Prime factorization of 69840 in exponential form is:

69840 = 2⁴ × 3² × 5¹ × 97¹

Step-3: Factors of 69825

List of positive integer factors of 69825 that divides 69825 without a remainder.

1, 3, 5, 7, 15, 19, 21, 25, 35, 49, 57, 75, 95, 105, 133, 147, 175, 245, 285, 399, 475, 525, 665, 735, 931, 1225, 1425, 1995, 2793, 3325, 3675, 4655, 9975, 13965, 23275

Step-4: Factors of 69840

List of positive integer factors of 69840 that divides 69825 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 97, 120, 144, 180, 194, 240, 291, 360, 388, 485, 582, 720, 776, 873, 970, 1164, 1455, 1552, 1746, 1940, 2328, 2910, 3492, 3880, 4365, 4656, 5820, 6984, 7760, 8730, 11640, 13968, 17460, 23280, 34920

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 69825 and 69840. The biggest common factor number is the GCF number.
So the greatest common factor 69825 and 69840 is 15.

Also check out the Least Common Multiple of 69825 and 69840