Chapter 3 Class 6 Playing with Numbers
Concept wise

If Sum of all factors is equal to twice the number,

then number is called a perfect number

#### For 6

Factors of 6 are 1, 2, 3, 6

Sum of factors = 1 + 2 + 3 + 6 = 12

Since 12 = 2 × 6

∴ Sum of factors is equal to twice the number

So, 6 is a perfect number

#### For 28

Factors of 28 are 1, 2, 4, 7, 14, 28

Sum of factors = 1 + 2 + 4 + 7 + 14 + 28 = 56

Since 56 = 2 × 28

∴ Sum of factors is equal to twice the number

So, 28 is a perfect number

#### For 10

Factors of 10 are 1, 2, 5, 10

Sum of factors = 1 + 2 + 5 + 10 = 18

Since 18 is not twice of 10

So, 10 is not a perfect number

## First 10 perfect numbers are

6

28

496

8128

33550336

8589869056

137438691328

2305843008139952128

2658455991569831744654692615953842176

191561942608236107294793378084303638130997321548169216

#### Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.