What is the Greatest Common Factor of 17765 and 17776?

Greatest common factor (GCF) of 17765 and 17776 is 11.

GCF(17765,17776) = 11

We will now calculate the prime factors of 17765 and 17776, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17765 and 17776.

How to find the GCF of 17765 and 17776?

We will first find the prime factorization of 17765 and 17776. After we will calculate the factors of 17765 and 17776 and find the biggest common factor number .

Step-1: Prime Factorization of 17765

Prime factors of 17765 are 5, 11, 17, 19. Prime factorization of 17765 in exponential form is:

17765 = 5¹ × 11¹ × 17¹ × 19¹

Step-2: Prime Factorization of 17776

Prime factors of 17776 are 2, 11, 101. Prime factorization of 17776 in exponential form is:

17776 = 2⁴ × 11¹ × 101¹

Step-3: Factors of 17765

List of positive integer factors of 17765 that divides 17765 without a remainder.

1, 5, 11, 17, 19, 55, 85, 95, 187, 209, 323, 935, 1045, 1615, 3553

Step-4: Factors of 17776

List of positive integer factors of 17776 that divides 17765 without a remainder.

1, 2, 4, 8, 11, 16, 22, 44, 88, 101, 176, 202, 404, 808, 1111, 1616, 2222, 4444, 8888

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17765 and 17776. The biggest common factor number is the GCF number.
So the greatest common factor 17765 and 17776 is 11.

Also check out the Least Common Multiple of 17765 and 17776