What is the Greatest Common Factor of 7126 and 7140?

Greatest common factor (GCF) of 7126 and 7140 is 14.

GCF(7126,7140) = 14

We will now calculate the prime factors of 7126 and 7140, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7126 and 7140.

How to find the GCF of 7126 and 7140?

We will first find the prime factorization of 7126 and 7140. After we will calculate the factors of 7126 and 7140 and find the biggest common factor number .

Step-1: Prime Factorization of 7126

Prime factors of 7126 are 2, 7, 509. Prime factorization of 7126 in exponential form is:

7126 = 2¹ × 7¹ × 509¹

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 7126

List of positive integer factors of 7126 that divides 7126 without a remainder.

1, 2, 7, 14, 509, 1018, 3563

Step-4: Factors of 7140

List of positive integer factors of 7140 that divides 7126 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 7126 and 7140. The biggest common factor number is the GCF number.
So the greatest common factor 7126 and 7140 is 14.

Also check out the Least Common Multiple of 7126 and 7140