Look at the following pattern. i) 28 = 22 × 71 ; Total number of fa

1.	Look at the following pattern. i) 28 = 22 × 71 ; Total number of factors (2+ 1)(1 + 1) = 3 × 2 = 6 28 is divisible by 6 factors i.e., 1, 2, 4, 7, 14, 28. ii) 30 = 21 × 31 × 51 , Total number of . factors (1 + 1) (1 + 1) (1 + 1) = 2 × 2 × 2 = 8 30 Is divisible by 8 factors i.e., 1, 2, 3, 5, 6, 10, 15 and 30 Find the pattern.
Answer» 24 = 2³ × 3¹ 24 has (3+1) (1 + 1) = 4 × 2 = 8 factors [1, 2, 3, 4, 6, 8, 12 and 24] 36 = 2² × 3² Number of factors = (2 + 1) (2 + 1) 3 × 3 = 9 [ 1, 2, 3. 4, 6, 9, 12, 18 and 36] If N = a^p . b^q . c^r …….. where N is a natural number. a. b, c … are primes and p, q, r ……. are positive integers then, the number of factors of N =(p- 1) (q+ 1)(r + 1)

Look at the following pattern. i) 28 = 22 × 71 ; Total number of factors (2+ 1)(1 + 1) = 3 × 2 = 6 28 is divisible by 6 factors i.e., 1, 2, 4, 7, 14, 28. ii) 30 = 21 × 31 × 51 , Total number of . factors (1 + 1) (1 + 1) (1 + 1) = 2 × 2 × 2 = 8 30 Is divisible by 8 factors i.e., 1, 2, 3, 5, 6, 10, 15 and 30 Find the pattern.

Answer»

24 = 2³ × 3¹

24 has (3+1) (1 + 1) = 4 × 2 = 8 factors

[1, 2, 3, 4, 6, 8, 12 and 24]

36 = 2² × 3²

Number of factors = (2 + 1) (2 + 1)

3 × 3 = 9 [ 1, 2, 3. 4, 6, 9, 12, 18 and 36]

If N = a^p . b^q . c^r …….. where N is a natural number.

a. b, c … are primes and p, q, r ……. are positive integers then, the number of factors of N =(p- 1) (q+ 1)(r + 1)