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.
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