Find the prime factorization of each number. Use exponents in your answer, when it is he...

Find the prime factorization of each number. Use exponents in your answer, when it is helpful. See Examples 5 and 6.

385

Reference Examples 5

Use a factor tree to find the prime factorization of 210.

Strategy We will factor each number that we encounter as a product of two whole numbers (other than 1 and itself) until all the factors involved are prime.

Why The prime factorization of a whole number contains only prime numbers.

Reference Examples 6

Use a division ladder to find the prime factorization of 280.

Strategy We will perform repeated divisions by prime numbers until the final quotient is itself a prime number.

Why If a prime number is a factor of 280, it will divide 280 exactly.

Solution

It is helpful to begin with the smallest prime, 2, as the first trial divisor. Then, if necessary, try the primes 3, 5, 7, 11, 13, … in that order.