What is the Greatest Common Factor of 7824 and 7830?

Greatest common factor (GCF) of 7824 and 7830 is 6.

GCF(7824,7830) = 6

We will now calculate the prime factors of 7824 and 7830, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7824 and 7830.

How to find the GCF of 7824 and 7830?

We will first find the prime factorization of 7824 and 7830. After we will calculate the factors of 7824 and 7830 and find the biggest common factor number .

Step-1: Prime Factorization of 7824

Prime factors of 7824 are 2, 3, 163. Prime factorization of 7824 in exponential form is:

7824 = 2⁴ × 3¹ × 163¹

Step-2: Prime Factorization of 7830

Prime factors of 7830 are 2, 3, 5, 29. Prime factorization of 7830 in exponential form is:

7830 = 2¹ × 3³ × 5¹ × 29¹

Step-3: Factors of 7824

List of positive integer factors of 7824 that divides 7824 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 163, 326, 489, 652, 978, 1304, 1956, 2608, 3912

Step-4: Factors of 7830

List of positive integer factors of 7830 that divides 7824 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 29, 30, 45, 54, 58, 87, 90, 135, 145, 174, 261, 270, 290, 435, 522, 783, 870, 1305, 1566, 2610, 3915

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7824 and 7830. The biggest common factor number is the GCF number.
So the greatest common factor 7824 and 7830 is 6.

Also check out the Least Common Multiple of 7824 and 7830