What is the Greatest Common Factor of 85743 and 85749?

Greatest common factor (GCF) of 85743 and 85749 is 3.

GCF(85743,85749) = 3

We will now calculate the prime factors of 85743 and 85749, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 85743 and 85749.

How to find the GCF of 85743 and 85749?

We will first find the prime factorization of 85743 and 85749. After we will calculate the factors of 85743 and 85749 and find the biggest common factor number .

Step-1: Prime Factorization of 85743

Prime factors of 85743 are 3, 7, 1361. Prime factorization of 85743 in exponential form is:

85743 = 3² × 7¹ × 1361¹

Step-2: Prime Factorization of 85749

Prime factors of 85749 are 3, 101, 283. Prime factorization of 85749 in exponential form is:

85749 = 3¹ × 101¹ × 283¹

Step-3: Factors of 85743

List of positive integer factors of 85743 that divides 85743 without a remainder.

1, 3, 7, 9, 21, 63, 1361, 4083, 9527, 12249, 28581

Step-4: Factors of 85749

List of positive integer factors of 85749 that divides 85743 without a remainder.

1, 3, 101, 283, 303, 849, 28583

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 85743 and 85749. The biggest common factor number is the GCF number.
So the greatest common factor 85743 and 85749 is 3.

Also check out the Least Common Multiple of 85743 and 85749