What is the greatest common factor of 14 and 48?

Answer 1

To find the GCF of 2 or more numbers, list their factors:

14: 1, 2, 7, 14

48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

2 is the first (and in this case only, except for 1) factor that 14 and 48 have in common. So, 2 is the GCF.

The greatest common factor of two or more numbers is the greatest common divisor of all of them, meaning it's the largest positive integer that divides the numbers without remainders. One way to find the GCF is to use prime factorization. Rewrite each number as a product of all prime numbers. Then find the primes that the numbers have in common, multiply those factors together, and you have your GCF! In this example:

14

Start with 2, the first prime. 14 = 2 x 7. 7 is prime, so you can't go any further with that one.

48

Again, start with 2. 48 = 2 x 24. Keep going with 2 until it doesn't work anymore. 48 = 2 x 2 x 12. Keep going. 48 = 2 x 2 x 2 x 6. One more time. 48 = 2 x 2 x 2 x 2 x 3. 3 is prime. You've gone as far as you can go.

What prime factors do these numbers have in common? Just a 2! So 2 is the GCF of 14 and 48.

Prime factorization works with smaller numbers. There's another way to find GCFs more efficiently, and that's with a Euclidean algorithm. Divide 48 by 14 to get 3 with a remainder of 6. Divide 14 by the remainder 6 to get 2 with a remainder of 2. Then divide remainder 6 by remainder 2 to get a remainder of 0 which means that 2 is the GCF. Sounds more complicated than it is!
The GCF is 2.