Question

find the prime factorization of 56. start with the least prime factor. the prime factorization of 56 is 56 = 2×2××× = 2×××. a number is greater than 2 and it has 2 as a factor. is the number prime or composite? explain. convince me!

Explanation:

Step1: Recall prime - composite definition

A prime number has only two distinct positive divisors: 1 and itself. A composite number has more than two positive divisors. Since the number has 2 as a factor and is greater than 2, it has at least 1, 2, and the number itself as factors. So it is composite.

Step2: Start prime - factorization of 56

Divide 56 by the smallest prime number 2. $56\div2 = 28$.

Step3: Divide 28 by 2 again

$28\div2=14$.

Step4: Divide 14 by 2

$14\div2 = 7$.

Step5: Write prime - factorization

Since 7 is a prime number, the prime - factorization of 56 is $56=2\times2\times2\times7$.

Answer:

The number is composite because it has a factor of 2 and is greater than 2, so it has more than two factors. The prime - factorization of 56 is $2\times2\times2\times7$.