# Divisible by 7

This rule states that if the difference between twice the digit at units place and the number formed from the remaining digits of the given number is divisible by 7 then the whole number is divisible by 7.

For Example: Check whether 343 is divisible by 7 or not?

The last digit is 3.

Twice the last digit = 3 × 2 = 6

The remaining digit of the number is 34

So, 34 – 6 = 28

Now, 28 is divisible by 7 and it gives 4. Hence the number 343 is divisible by 7

Here are few examples on the divisibility rule of 7

1. Check whether the number are divisible by 7 or not?

(i) 153

(ii) 161

(iii) 855

(iv) 385

(v) 287

(vi) 644

(vii) 256

(viii) 536

(ix) 175

(x) 291

Solution:

(i) 153

Twice the last digit = 3 × 2 = 6

Remaining digits 15

Now, 15 – 6 = 9

9 is not divisible by 7 hence, 153 is not divisible by 7

(ii) 161

Twice the last digit = 1 × 2 = 2

Remaining digits = 16

So, 16 – 2 = 14

Now 14 is divisible by 7 hence 161 is also divisible by 7

(iii) 855

Twice the last digit = 5 × 2 = 10

85 is the remaining digit

So, 85 – 10  = 75

75 is not divisible by 7 hence, the number 855 is also not divisible by 7

(iv) 385

Twice the last digit = 5 × 2 = 10

Remaining digit = 38

So, 38 – 10 = 28

28 is divisible by 7 hence, 385 is also divisible by 7

(v) 287

Twice the last digit = 7 × 2 = 14

28 is the remaining digit

Hence, 28 – 14 = 7

7 is divisible by 7 hence, 287 is also divisible by 7

(vi) 644

Twice the last digit = 4 × 2 = 8

Remaining digit = 64

Now, 64 – 8 = 56

As, 56 is divisible by 7 hence, 287 is also divisible by 7

(vii) 256

Twice the last digit = 6 × 2 = 12

Remaining digits = 25

25 – 12 = 13

As, 13 is not divisible by 7 hence, 256 is also not divisible by 7

(viii) 536

Twice the last digit = 6 × 2 = 12

Remaining digit = 53

Now, 53 – 12 = 41

41 is not divisible by 7 hence the whole number is not divisible by 7

(ix) 175

Twice the last digit = 5 × 2 = 10

Remaining digit = 17

Now, 17 – 10 = 7

Hence, 175 is divisible by 7

(x) 291

Twice the last digit = 1 × 2 = 2

29 – 2 = 27

As, 27 is not divisible by 7 hence, 291 is also not divisible by 7

3. Rewrite the numbers with a different color which are divisible by 7

616        595          602          5633         791        2310         258

Solution:

616            595          602         5633         791         2310        258

The numbers colored in green are not divisible by 7 and the rest are divisible by 7

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