# Divisible by 7

Divisible by 7 is discussed below:

We need to double the last digit of the number and then subtract it from the remaining number. If the result is divisible by 7, then the original number will also be divisible by 7.

I: Consider the following numbers which are divisible by 7, using the test of divisibility by 7: 133, 273, 329, 595, 672.

(i) 133

In the number 133, double the last digit of the number 3 is 6. 13 – 6 = 7 [Now we need to subtract it from the rest of the remaining number]

Since 7 is divisible by 7.

Hence, 133 is also divisible by 7.

(ii) 273

In the number 273, double the last digit of the number 3 is 6. 27 – 6 = 21 [Now we need to subtract it from the rest of theremaining number]

Since 21 is divisible by 7.

Hence, 273 is also divisible by 7.

(iii) 329

In the number 329, double the last digit of the number 9 is 18. 32 – 18 = 14 [Now we need to subtract it from the rest of the remaining number]

Since 14 is divisible by 7.

Hence, 329 is also divisible by 7.

(iv) 595

In the number 595, double the last digit of the number 5 is 10. 59 – 10 = 49 [Now we need to subtract it from the rest of the remaining number]

Since 49 is divisible by 7.

Hence, 595 is also divisible by 7.

(v) 672

In the number 672, double the last digit of the number 2 is 4. 67 – 4 = 63 [Now we need to subtract it from the rest of the remaining number]

Since 63 is divisible by 7.

Hence, 672 is also divisible by 7.

II: Consider the following numbers which are not divisible by 7, using the rules of divisibility by 7: 167, 233, 297, 305,317.

(i) 167

In the number 167, double the last digit of the number 7 is 14. 16 – 14 = 2 [Now we need to subtract it from the rest of the remaining number]

Since 2 is not divisible by 7.

Hence, 167 is also not divisible by 7.

(ii) 233

In the number 233, double the last digit of the number 3 is 6. 23 – 6 = 17 [Now we need to subtract it from the rest of the remaining number]

Since 17 is not divisible by 7.

Hence, 233 is also not divisible by 7.

(iii)297

In the number 297, double the last digit of the number 7 is 14. 29 – 14 = 15 [Now we need to subtract it from the rest of the remaining number]

Since 15 is not divisible by 7.

Hence, 297 is also not divisible by 7.

(iv) 305

In the number 305, double the last digit of the number 5 is 10. 30 – 10 = 20 [Now we need to subtract it from the rest of the remaining number]

Since 20 is not divisible by 7.

Hence, 305 is also not divisible by 7.

(v) 317

In the number 317, double the last digit of the number 7 is 14. 31 – 14 = 17 [Now we need to subtract it from the rest of the remaining number]

Since 17 is not divisible by 7.

Hence, 317 is also not divisible by 7.

Properties of Divisibility.

Divisible by 2.

Divisible by 3.

Divisible by 4.

Divisible by 5.

Divisible by 6.

Divisible by 7.

Divisible by 8.

Divisible by 9.

Divisible by 10.

Problems on Divisibility Rules

Worksheet on Divisibility Rules

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