What is the Greatest Common Factor of 1743 and 1757?

Greatest common factor (GCF) of 1743 and 1757 is 7.

GCF(1743,1757) = 7

We will now calculate the prime factors of 1743 and 1757, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1743 and 1757.

How to find the GCF of 1743 and 1757?

We will first find the prime factorization of 1743 and 1757. After we will calculate the factors of 1743 and 1757 and find the biggest common factor number .

Step-1: Prime Factorization of 1743

Prime factors of 1743 are 3, 7, 83. Prime factorization of 1743 in exponential form is:

1743 = 3¹ × 7¹ × 83¹

Step-2: Prime Factorization of 1757

Prime factors of 1757 are 7, 251. Prime factorization of 1757 in exponential form is:

1757 = 7¹ × 251¹

Step-3: Factors of 1743

List of positive integer factors of 1743 that divides 1743 without a remainder.

1, 3, 7, 21, 83, 249, 581

Step-4: Factors of 1757

List of positive integer factors of 1757 that divides 1743 without a remainder.

1, 7, 251

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1743 and 1757. The biggest common factor number is the GCF number.
So the greatest common factor 1743 and 1757 is 7.

Also check out the Least Common Multiple of 1743 and 1757