Maths Olympiad Prep

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Number theory Difficulty 2.4 Junior Find the answer

The integer 119 is a multiple of which number?

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

The ones digit of 119 is not even, so 119 is not a multiple of 2. The ones digit of 119 is not 0 or 5, so 119 is not a multiple of 5. Since 120=3×40120=3 \times 40, then 119 is 1 less than a multiple of 3 so is not itself a multiple of 3. Since 110=11×10110=11 \times 10 and 121=11×11121=11 \times 11, then 119 is between two consecutive multiples of 11, so is not itself a multiple of 11. Finally, 119÷7=17119 \div 7=17, so 119 is a multiple of 7.

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Source: Omni-MATH, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.