What is the Greatest Common Factor of 39814 and 39825?

Greatest common factor (GCF) of 39814 and 39825 is 1.

GCF(39814,39825) = 1

We will now calculate the prime factors of 39814 and 39825, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39814 and 39825.

How to find the GCF of 39814 and 39825?

We will first find the prime factorization of 39814 and 39825. After we will calculate the factors of 39814 and 39825 and find the biggest common factor number .

Step-1: Prime Factorization of 39814

Prime factors of 39814 are 2, 17, 1171. Prime factorization of 39814 in exponential form is:

39814 = 2¹ × 17¹ × 1171¹

Step-2: 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-3: Factors of 39814

List of positive integer factors of 39814 that divides 39814 without a remainder.

1, 2, 17, 34, 1171, 2342, 19907

Step-4: Factors of 39825

List of positive integer factors of 39825 that divides 39814 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39814 and 39825. The biggest common factor number is the GCF number.
So the greatest common factor 39814 and 39825 is 1.

Also check out the Least Common Multiple of 39814 and 39825