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.
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.
By dividing 90 by every integer from 1 upwards:
90 ÷ 1 = 90 ✓ 90 ÷ 2 = 45 ✓ 90 ÷ 3 = 30 ✓ 90 ÷ 5 = 18 ✓ 90 ÷ 6 = 15 ✓ 90 ÷ 9 = 10 ✓ 90 ÷ 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
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):
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.
Factors of 15 and Prime Factorization
Learn how to find the factors of 15. Discover its prime factors, factor pairs, and understand why 15 is a composite number.
Factors of 20 and Prime Factorization
Learn how to easily calculate the factors of 20. Find out the positive and negative factor pairs and the prime factorization using a factor tree.
What are the Factors of 27?
Learn how to find all the factors of 27. See the step-by-step division method, the factor pairs, and the prime factorization of 27.
Factors of 35 and Prime Factorization
Learn how to find all the factors of 35. Discover its prime factorization and understand why it only has four factors.
What are the Factors of 54?
Learn how to calculate all the factors of 54. Understand the factor pairs, step-by-step division rules, and the prime factorization of 54.
Turn this guide into revision flashcards, a practice exam, or an AI-generated podcast — free, no signup required.