What is the Greatest Common Factor of 7830 and 7842?

Greatest common factor (GCF) of 7830 and 7842 is 6.

GCF(7830,7842) = 6

We will now calculate the prime factors of 7830 and 7842, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7830 and 7842.

How to find the GCF of 7830 and 7842?

We will first find the prime factorization of 7830 and 7842. After we will calculate the factors of 7830 and 7842 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 7842

Prime factors of 7842 are 2, 3, 1307. Prime factorization of 7842 in exponential form is:

7842 = 2¹ × 3¹ × 1307¹

Step-3: Factors of 7830

List of positive integer factors of 7830 that divides 7830 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

Step-4: Factors of 7842

List of positive integer factors of 7842 that divides 7830 without a remainder.

1, 2, 3, 6, 1307, 2614, 3921

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7830 and 7842. The biggest common factor number is the GCF number.
So the greatest common factor 7830 and 7842 is 6.

Also check out the Least Common Multiple of 7830 and 7842