What is the Greatest Common Factor of 31814 and 31830?

Greatest common factor (GCF) of 31814 and 31830 is 2.

GCF(31814,31830) = 2

We will now calculate the prime factors of 31814 and 31830, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31814 and 31830.

How to find the GCF of 31814 and 31830?

We will first find the prime factorization of 31814 and 31830. After we will calculate the factors of 31814 and 31830 and find the biggest common factor number .

Step-1: Prime Factorization of 31814

Prime factors of 31814 are 2, 15907. Prime factorization of 31814 in exponential form is:

31814 = 2¹ × 15907¹

Step-2: Prime Factorization of 31830

Prime factors of 31830 are 2, 3, 5, 1061. Prime factorization of 31830 in exponential form is:

31830 = 2¹ × 3¹ × 5¹ × 1061¹

Step-3: Factors of 31814

List of positive integer factors of 31814 that divides 31814 without a remainder.

1, 2, 15907

Step-4: Factors of 31830

List of positive integer factors of 31830 that divides 31814 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30, 1061, 2122, 3183, 5305, 6366, 10610, 15915

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31814 and 31830. The biggest common factor number is the GCF number.
So the greatest common factor 31814 and 31830 is 2.

Also check out the Least Common Multiple of 31814 and 31830