What is the Greatest Common Factor of 29640 and 29648?

Greatest common factor (GCF) of 29640 and 29648 is 8.

GCF(29640,29648) = 8

We will now calculate the prime factors of 29640 and 29648, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29640 and 29648.

How to find the GCF of 29640 and 29648?

We will first find the prime factorization of 29640 and 29648. After we will calculate the factors of 29640 and 29648 and find the biggest common factor number .

Step-1: Prime Factorization of 29640

Prime factors of 29640 are 2, 3, 5, 13, 19. Prime factorization of 29640 in exponential form is:

29640 = 2³ × 3¹ × 5¹ × 13¹ × 19¹

Step-2: Prime Factorization of 29648

Prime factors of 29648 are 2, 17, 109. Prime factorization of 29648 in exponential form is:

29648 = 2⁴ × 17¹ × 109¹

Step-3: Factors of 29640

List of positive integer factors of 29640 that divides 29640 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 19, 20, 24, 26, 30, 38, 39, 40, 52, 57, 60, 65, 76, 78, 95, 104, 114, 120, 130, 152, 156, 190, 195, 228, 247, 260, 285, 312, 380, 390, 456, 494, 520, 570, 741, 760, 780, 988, 1140, 1235, 1482, 1560, 1976, 2280, 2470, 2964, 3705, 4940, 5928, 7410, 9880, 14820

Step-4: Factors of 29648

List of positive integer factors of 29648 that divides 29640 without a remainder.

1, 2, 4, 8, 16, 17, 34, 68, 109, 136, 218, 272, 436, 872, 1744, 1853, 3706, 7412, 14824

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29640 and 29648. The biggest common factor number is the GCF number.
So the greatest common factor 29640 and 29648 is 8.

Also check out the Least Common Multiple of 29640 and 29648