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(ii) 8 is a deficient number.

As, proper divisors of 8 = 1, 2 and 4
And, sum of its proper divisors = 1 + 2 + 4 = 7 < 8
Hence, 8 is a deficient number.
Amicable Numbers

In mathematics, amicable numbers are a pair of numbers such that the sum of the proper divisors
of one number is equal to the other number and vice versa.
For example: 220 and 284 are amicable numbers.
As, proper divisors of 220 = 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110,

And, sum of proper divisors of 220 = 1 + 2 + 4 + 5 + 10 + 11 + 20 + 22 + 44 + 55 + 110 = 284
Proper divisors of 284 = 1, 2, 4, 71 and 142
Sum of proper divisors of 284 = 1 + 2 + 4 + 71 + 142 = 220

(220, 284), (1184, 1210), (2620, 2924), (5020, 5564), (6232, 6368), (10744, 10856) are some amicable
pairs of numbers.
Practice Time 5D

1. Complete the factor tree.

(a) 72 (b) 450 (c) 50 (d) 81

2. Find the prime factorisation of the following numbers by factor tree method.
(a) 105 (b) 1728 (c) 1024 (d) 729

3. Find the prime factorisation of the following using the division method.
(a) 141 (b) 1000 (c) 1331 (d) 625

4. What is the smallest number whose prime factorisation has:
(a) Three different prime numbers?
(b) Five different prime numbers?

5. Using the method of prime factorisation, check whether the given pair is co-prime or not.
(a) (25, 56) (b) (231, 242) (c) (75, 78) (d) (102, 110)
6. Write an example for each of perfect number, abundant number and deficient number.

7. Write a pair of amicable numbers and find their proper divisors to check whether the statement of
amicable numbers is correct.

153 Prime Time