Study Guides/Maths/Factors of 90
Study Guide · Maths

Factors of 90 — All Factor Pairs Listed

The factors of 90 are all the integers that divide 90 exactly without leaving any remainder. Finding factors is a fundamental skill in mathematics that applies to HCF, LCM, fractions, and number theory.

Question (Click to Flip)

Is 90 a perfect square?

Answer

No, 90 is not a perfect square. Its prime factorization is 2¹ × 3² × 5¹. For a perfect square, all prime factors must appear an even number of times. Since 2 and 5 appear only once (odd), 90 is not a perfect square.

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Key Facts

To find the total number of factors using prime factorization: If n = 2¹ × 3² × 5¹, then the number of factors = (1+1)(2+1)(1+1) = 2 × 3 × 2 = 12 factors.

All Factors of 90

By dividing 90 by every integer from 1 upwards:

90 ÷ 1 = 9090 ÷ 2 = 4590 ÷ 3 = 3090 ÷ 5 = 1890 ÷ 6 = 1590 ÷ 9 = 1090 ÷ 10 = 9

Complete list of all factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90

Total number of factors = 12

Prime Factorization of 90

Using the factor tree or division method:

90 = 2 × 45 45 = 3 × 15 15 = 3 × 5

Therefore: 90 = 2¹ × 3² × 5¹

Factor Pairs of 90 (pairs that multiply to give 90):

  • 1 × 90
  • 2 × 45
  • 3 × 30
  • 5 × 18
  • 6 × 15
  • 9 × 10

Questions and Answers

Is 90 a perfect square?+

No, 90 is not a perfect square. Its prime factorization is 2¹ × 3² × 5¹. For a perfect square, all prime factors must appear an even number of times. Since 2 and 5 appear only once (odd), 90 is not a perfect square.

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