What is the Greatest Common Factor of 7840 and 7854?

Greatest common factor (GCF) of 7840 and 7854 is 14.

GCF(7840,7854) = 14

We will now calculate the prime factors of 7840 and 7854, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7840 and 7854.

How to find the GCF of 7840 and 7854?

We will first find the prime factorization of 7840 and 7854. After we will calculate the factors of 7840 and 7854 and find the biggest common factor number .

Step-1: Prime Factorization of 7840

Prime factors of 7840 are 2, 5, 7. Prime factorization of 7840 in exponential form is:

7840 = 2⁵ × 5¹ × 7²

Step-2: Prime Factorization of 7854

Prime factors of 7854 are 2, 3, 7, 11, 17. Prime factorization of 7854 in exponential form is:

7854 = 2¹ × 3¹ × 7¹ × 11¹ × 17¹

Step-3: Factors of 7840

List of positive integer factors of 7840 that divides 7840 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 32, 35, 40, 49, 56, 70, 80, 98, 112, 140, 160, 196, 224, 245, 280, 392, 490, 560, 784, 980, 1120, 1568, 1960, 3920

Step-4: Factors of 7854

List of positive integer factors of 7854 that divides 7840 without a remainder.

1, 2, 3, 6, 7, 11, 14, 17, 21, 22, 33, 34, 42, 51, 66, 77, 102, 119, 154, 187, 231, 238, 357, 374, 462, 561, 714, 1122, 1309, 2618, 3927

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7840 and 7854. The biggest common factor number is the GCF number.
So the greatest common factor 7840 and 7854 is 14.

Also check out the Least Common Multiple of 7840 and 7854