What is the Greatest Common Factor of 7140 and 7160?

Greatest common factor (GCF) of 7140 and 7160 is 20.

GCF(7140,7160) = 20

We will now calculate the prime factors of 7140 and 7160, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7140 and 7160.

How to find the GCF of 7140 and 7160?

We will first find the prime factorization of 7140 and 7160. After we will calculate the factors of 7140 and 7160 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 7160

Prime factors of 7160 are 2, 5, 179. Prime factorization of 7160 in exponential form is:

7160 = 2³ × 5¹ × 179¹

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 7160

List of positive integer factors of 7160 that divides 7140 without a remainder.

1, 2, 4, 5, 8, 10, 20, 40, 179, 358, 716, 895, 1432, 1790, 3580

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7140 and 7160. The biggest common factor number is the GCF number.
So the greatest common factor 7140 and 7160 is 20.

Also check out the Least Common Multiple of 7140 and 7160