What is the Greatest Common Factor of 1742 and 1760?

Greatest common factor (GCF) of 1742 and 1760 is 2.

GCF(1742,1760) = 2

We will now calculate the prime factors of 1742 and 1760, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1742 and 1760.

How to find the GCF of 1742 and 1760?

We will first find the prime factorization of 1742 and 1760. After we will calculate the factors of 1742 and 1760 and find the biggest common factor number .

Step-1: Prime Factorization of 1742

Prime factors of 1742 are 2, 13, 67. Prime factorization of 1742 in exponential form is:

1742 = 2¹ × 13¹ × 67¹

Step-2: Prime Factorization of 1760

Prime factors of 1760 are 2, 5, 11. Prime factorization of 1760 in exponential form is:

1760 = 2⁵ × 5¹ × 11¹

Step-3: Factors of 1742

List of positive integer factors of 1742 that divides 1742 without a remainder.

1, 2, 13, 26, 67, 134, 871

Step-4: Factors of 1760

List of positive integer factors of 1760 that divides 1742 without a remainder.

1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 32, 40, 44, 55, 80, 88, 110, 160, 176, 220, 352, 440, 880

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1742 and 1760. The biggest common factor number is the GCF number.
So the greatest common factor 1742 and 1760 is 2.

Also check out the Least Common Multiple of 1742 and 1760