Question

Find the largest 2-digit number divisible by 7.

Answer 1

Hint: In this question, we will proceed by letting the largest 2-digit number. Then use Euclid's Division Lemma to know whether it is divisible by 7. If it is not divisible by 7 then consider the next 2-digit largest number and verify it is divisible by 7 or not by again using Euclid's Division Lemma. So, use this concept to reach the solution of the given problem.

Complete step by step answer:
Here we have to find the largest 2-digit number that is divisible by 7.
We know that the largest two-digit number is 99.
According to Euclid`s Division Lemma we have dividend = division \[ \times \]divisor \[ + \]remainder
On dividing 99 with 7, we have quotient as 14 and remainder 1 i.e., \[99 = 14 \times 7 + 1\]
So, 99 is not the largest 2-digit number that is divisible by 7.
Now, consider the next largest two-digit number i.e., 98.
On dividing 98 with 7, we have quotient as 14 and remainder 0 i.e., \[98 = 14 \times 7 + 0\]
So, 98 is the largest 2-digit number that is divisible by 7.

Thus, the largest 2-digit number divisible by 7 is 98.

Note: In Mathematics, Euclidean division with remainder is the process of dividing one integer by another, in such a way that produces a quotient and a remainder smaller than the divisor.