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Factors, GCF, LCM & Division • Lesson 17 ⏱ 6 min read 📅 Updated Nov 2026

Factors, Factor Pairs, and Prime Numbers: A Visual Guide

Learn what factors are, how to find all factor pairs of a number, the Sieve of Eratosthenes, and the Fundamental Theorem of Arithmetic.

Core Concept

A factor is a whole number that divides into another number with zero remainder. Factors always come in pairs.

36 6 6 2 3 2 3 Prime Leaves: 36 = 2 × 2 × 3 × 3 = 2² × 3²
Complete Factor Tree: Branch Downwards Until Only Green Prime Leaves Remain

Factor Pairs of 36 (Testing up to √(36) = 6)

DivisorCalculationFactor Pair
136 ÷ 1 = 36(1, 36)
236 ÷ 2 = 18(2, 18)
336 ÷ 3 = 12(3, 12)
436 ÷ 4 = 9(4, 9)
636 ÷ 6 = 6(6, 6) • Perfect Square!

Prime vs. Composite

  • Prime Numbers (Exactly 2 factors): 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31…
  • Composite Numbers (3+ factors): 4, 6, 8, 9, 10, 12, 14, 15, 16, 18…
Try It Yourself

Practice with Our Interactive Factors Calculator

Check your calculations or explore full step-by-step solutions instantly.

Open Factors Calculator →
Solved Step-by-Step Examples:Factors of 36Factors of 48Factors of 60
Your Turn!

Check Your Understanding (3 Quick Questions)

Score: 0 / 3

Question 1: How many total factors does the number 12 have?

Question 2: Why is 1 NOT a prime number?

Question 3: Which is the ONLY even prime number in mathematics?