How to Find the Factors of 90

Factors are numbers that divide another number completely, leaving no remainder. To find the factors of 90, follow these steps:

Step 1: Understand Factors

• A factor of 90 is any number that divides 90 exactly.
• Factors come in pairs (e.g., $1\times 90$, 2×45, etc.).

Step 2: List All Factor Pairs

• Start dividing 90 by smaller numbers:
  • 90÷1= 90 → Factors: 11 and 9090.
  • 90÷2 = 45 → Factors: 22 and 4545.
  • 90÷3 = 30 → Factors: 33 and 3030.
  • 90÷5 = 18 → Factors: 55 and 1818.
  • 90÷6 = 15 → Factors: 66 and 1515.
  • 90÷9 = 10 → Factors: 99 and 1010.

Step 3: List All Unique Factors

The factors of 90 are:
1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90

Step 4: Verify

Multiply any two numbers from a factor pair to confirm they equal 90.
Example: 6×15 = 90, 3×30 = 90, etc.

Prime Factorization (Optional)

Breaking 90 into prime factors:

• 90÷2= 45 → Prime factor: 22
• 45÷3= 15 → Prime factor: 33
• 15÷3 = 5 → Prime factor: 33
• Remaining: 55 → Prime factor: 55

Prime factorization: 90=2×3×3×5