# 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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**5th Grade Math**

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