What is the Greatest Common Factor of 7130 and 7140?

Greatest common factor (GCF) of 7130 and 7140 is 10.

GCF(7130,7140) = 10

We will now calculate the prime factors of 7130 and 7140, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7130 and 7140.

How to find the GCF of 7130 and 7140?

We will first find the prime factorization of 7130 and 7140. After we will calculate the factors of 7130 and 7140 and find the biggest common factor number .

Step-1: Prime Factorization of 7130

Prime factors of 7130 are 2, 5, 23, 31. Prime factorization of 7130 in exponential form is:

7130 = 2¹ × 5¹ × 23¹ × 31¹

Step-2: 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-3: Factors of 7130

List of positive integer factors of 7130 that divides 7130 without a remainder.

1, 2, 5, 10, 23, 31, 46, 62, 115, 155, 230, 310, 713, 1426, 3565

Step-4: Factors of 7140

List of positive integer factors of 7140 that divides 7130 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7130 and 7140. The biggest common factor number is the GCF number.
So the greatest common factor 7130 and 7140 is 10.

Also check out the Least Common Multiple of 7130 and 7140