What is the Greatest Common Factor of 1785 and 1792?

Greatest common factor (GCF) of 1785 and 1792 is 7.

GCF(1785,1792) = 7

We will now calculate the prime factors of 1785 and 1792, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1785 and 1792.

How to find the GCF of 1785 and 1792?

We will first find the prime factorization of 1785 and 1792. After we will calculate the factors of 1785 and 1792 and find the biggest common factor number .

Step-1: Prime Factorization of 1785

Prime factors of 1785 are 3, 5, 7, 17. Prime factorization of 1785 in exponential form is:

1785 = 3¹ × 5¹ × 7¹ × 17¹

Step-2: Prime Factorization of 1792

Prime factors of 1792 are 2, 7. Prime factorization of 1792 in exponential form is:

1792 = 2⁸ × 7¹

Step-3: Factors of 1785

List of positive integer factors of 1785 that divides 1785 without a remainder.

1, 3, 5, 7, 15, 17, 21, 35, 51, 85, 105, 119, 255, 357, 595

Step-4: Factors of 1792

List of positive integer factors of 1792 that divides 1785 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 128, 224, 256, 448, 896

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1785 and 1792. The biggest common factor number is the GCF number.
So the greatest common factor 1785 and 1792 is 7.

Also check out the Least Common Multiple of 1785 and 1792