Problem 1 · 2020 Math Kangaroo
Medium
Number Theory
last-digitmod-10
What is the last digit of the product \(1 \times 3 \times 5 \times 7 \times 9^2 \times 7 \times 5 \times 3 \times 1\)?
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Answer: C — 5
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Hint 1 of 2
The product is a string of odd factors — is any of them a 5?
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Hint 2 of 2
An odd number times 5 always ends in 5.
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Approach: spot the factor 5 among odd numbers
- Every factor in the product is odd, and one of them is 5.
- An odd multiple of 5 always ends in the digit 5.
- So the last digit of the whole product is 5.
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