What is the Greatest Common Factor of 7140 and 7146?

Greatest common factor (GCF) of 7140 and 7146 is 6.

GCF(7140,7146) = 6

We will now calculate the prime factors of 7140 and 7146, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7140 and 7146.

How to find the GCF of 7140 and 7146?

We will first find the prime factorization of 7140 and 7146. After we will calculate the factors of 7140 and 7146 and find the biggest common factor number .

Step-1: Prime Factorization of 7140

Prime factors of 7140 are 2, 3, 5, 7, 17. Prime factorization of 7140 in exponential form is:

7140 = 2² × 3¹ × 5¹ × 7¹ × 17¹

Step-2: Prime Factorization of 7146

Prime factors of 7146 are 2, 3, 397. Prime factorization of 7146 in exponential form is:

7146 = 2¹ × 3² × 397¹

Step-3: Factors of 7140

List of positive integer factors of 7140 that divides 7140 without a remainder.

1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 17, 20, 21, 28, 30, 34, 35, 42, 51, 60, 68, 70, 84, 85, 102, 105, 119, 140, 170, 204, 210, 238, 255, 340, 357, 420, 476, 510, 595, 714, 1020, 1190, 1428, 1785, 2380, 3570

Step-4: Factors of 7146

List of positive integer factors of 7146 that divides 7140 without a remainder.

1, 2, 3, 6, 9, 18, 397, 794, 1191, 2382, 3573

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7140 and 7146. The biggest common factor number is the GCF number.
So the greatest common factor 7140 and 7146 is 6.

Also check out the Least Common Multiple of 7140 and 7146