Question

Test the divisibility of the following numbers by $7:$
(i) $826$
(ii) $117$
(iii) $2345$
(iv) $6021$
(v) $14126$
(vi) $25368$

Answer 1

To determine if a number is divisible by $7$, double the last digit of the number and subtract it from the number formed by the remaining digits. If their difference is a multiple of $7$, the number is divisible by $7.$
(i) $826$ is divisible by $7.$
We have $82-(2\times 6)=70$, which is a multiple of $7.$
(ii) $117$ is not divisible by $7.$
We have $11-(2\times 7)=-3$, which is not a multiple of $7$.
(iii) $2345$ is divisible by $7.$
We have $234-(2\times 5)=224,$ which is a multiple of $7$.
(iv) $6021$ is divisible by $7.$
We have $602-(2\times 1)=600,$ which is not a multiple of $7.$
(v) $14126$ is divisible by $7.$
We have $1412-(2\times 6)=1400,$ which is a multiple of $7.$
(vi) $25368$ is divisible by $7.$
We have $2536-(2\times 8)=2520,$ which is a multiple of $7.$