AlgebraStructure & Method · Book 1All Chapters

Quotients and Factoring

5-1Factoring Integers

Overview

Every integer > 1 can be written as a product of prime numbers (its prime factorization).

Key ideas

  • Primes: 2, 3, 5, 7, 11, 13, …
  • Use a factor tree or repeated division.
  • Greatest Common Factor (GCF) uses the smallest power of each shared prime.

Worked examples

Example 1

Problem. Prime factorization of 60.

Solution. 2^2 · 3 · 5

Example 2

Problem. GCF of 24 and 36.

Solution. 2^2 · 3 = 12

Practice

Try each one. Click Show answer when ready.

  1. 1.

    Prime factorization of 84.

  2. 2.

    GCF of 18 and 30.

  3. 3.

    GCF of 45 and 75.

Challenge problems

A little tougher — great for test prep. Click Show answer when ready.

  1. 1.

    Find the GCF of 72, 96, and 120.

  2. 2.

    Express 180 as a product of prime factors.