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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