What is the Greatest Common Factor of 17640 and 17654?

Greatest common factor (GCF) of 17640 and 17654 is 14.

GCF(17640,17654) = 14

We will now calculate the prime factors of 17640 and 17654, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17640 and 17654.

How to find the GCF of 17640 and 17654?

We will first find the prime factorization of 17640 and 17654. After we will calculate the factors of 17640 and 17654 and find the biggest common factor number .

Step-1: Prime Factorization of 17640

Prime factors of 17640 are 2, 3, 5, 7. Prime factorization of 17640 in exponential form is:

17640 = 2³ × 3² × 5¹ × 7²

Step-2: Prime Factorization of 17654

Prime factors of 17654 are 2, 7, 13, 97. Prime factorization of 17654 in exponential form is:

17654 = 2¹ × 7¹ × 13¹ × 97¹

Step-3: Factors of 17640

List of positive integer factors of 17640 that divides 17640 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 21, 24, 28, 30, 35, 36, 40, 42, 45, 49, 56, 60, 63, 70, 72, 84, 90, 98, 105, 120, 126, 140, 147, 168, 180, 196, 210, 245, 252, 280, 294, 315, 360, 392, 420, 441, 490, 504, 588, 630, 735, 840, 882, 980, 1176, 1260, 1470, 1764, 1960, 2205, 2520, 2940, 3528, 4410, 5880, 8820

Step-4: Factors of 17654

List of positive integer factors of 17654 that divides 17640 without a remainder.

1, 2, 7, 13, 14, 26, 91, 97, 182, 194, 679, 1261, 1358, 2522, 8827

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17640 and 17654. The biggest common factor number is the GCF number.
So the greatest common factor 17640 and 17654 is 14.

Also check out the Least Common Multiple of 17640 and 17654