Find the largest 5-digit number that is exactly divisible by 91.

Given data

• We need the greatest multiple of 91 that does not exceed 99,999.

Concept / Approach

• Compute ⌊99999 ÷ 91⌋ and multiply back by 91.

Step-by-step calculation

91 × 1100 = 100,100 (too large)So try 1100 − 2 = 1098 ⇒ 91 × 1098 = 100,100 − 182 = 99,918

Verification

99,918 + 91 = 100,009 > 99,999 ⇒ 99,918 is indeed the largest 5-digit multiple.

Final Answer

Largest 5-digit multiple of 91 is 99,918.