What is the Greatest Common Factor of 7814 and 7820?

Greatest common factor (GCF) of 7814 and 7820 is 2.

GCF(7814,7820) = 2

We will now calculate the prime factors of 7814 and 7820, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7814 and 7820.

How to find the GCF of 7814 and 7820?

We will first find the prime factorization of 7814 and 7820. After we will calculate the factors of 7814 and 7820 and find the biggest common factor number .

Step-1: Prime Factorization of 7814

Prime factors of 7814 are 2, 3907. Prime factorization of 7814 in exponential form is:

7814 = 2¹ × 3907¹

Step-2: Prime Factorization of 7820

Prime factors of 7820 are 2, 5, 17, 23. Prime factorization of 7820 in exponential form is:

7820 = 2² × 5¹ × 17¹ × 23¹

Step-3: Factors of 7814

List of positive integer factors of 7814 that divides 7814 without a remainder.

1, 2, 3907

Step-4: Factors of 7820

List of positive integer factors of 7820 that divides 7814 without a remainder.

1, 2, 4, 5, 10, 17, 20, 23, 34, 46, 68, 85, 92, 115, 170, 230, 340, 391, 460, 782, 1564, 1955, 3910

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7814 and 7820. The biggest common factor number is the GCF number.
So the greatest common factor 7814 and 7820 is 2.

Also check out the Least Common Multiple of 7814 and 7820