What is the Greatest Common Factor of 39825 and 39830?

Greatest common factor (GCF) of 39825 and 39830 is 5.

GCF(39825,39830) = 5

We will now calculate the prime factors of 39825 and 39830, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39825 and 39830.

How to find the GCF of 39825 and 39830?

We will first find the prime factorization of 39825 and 39830. After we will calculate the factors of 39825 and 39830 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 39830

Prime factors of 39830 are 2, 5, 7, 569. Prime factorization of 39830 in exponential form is:

39830 = 2¹ × 5¹ × 7¹ × 569¹

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 39830

List of positive integer factors of 39830 that divides 39825 without a remainder.

1, 2, 5, 7, 10, 14, 35, 70, 569, 1138, 2845, 3983, 5690, 7966, 19915

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39825 and 39830. The biggest common factor number is the GCF number.
So the greatest common factor 39825 and 39830 is 5.

Also check out the Least Common Multiple of 39825 and 39830