All even numbers from 2 to 98 inclusive, except those ending 0, are multiplied…
2026
All even numbers from 2 to 98 inclusive, except those ending 0, are multiplied together. What is the rightmost digit (the units digit) of the product?
- A.
5
- B.
0
- C.
6
- D.
7
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Correct answer: C
Original solution image: https://test-portal-assets.s3.ap-south-1.amazonaws.com/production_1598963827081/ee9f7458-0915-4229-a5f7-62534f8202dc.png
Key idea: find the units digit by multiplying the units digits of the included even numbers.
Count the factors: Even numbers from 2 to 98 inclusive are 49 numbers. Excluding those ending in 0 (10, 20, …, 90) removes 9 numbers, leaving 40 factors.
Units-digit pattern: In each block of ten (0–9, 10–19, …, 90–99) the included even numbers have units digits 2, 4, 6, 8. The product of these four units digits is 2×4×6×8 = 384, so the units digit for one decade is 4.
Total product: There are 10 such decades, so the product's units digit is 4^{10}. Powers of 4 alternate units digits 4, 6, 4, 6, …; since 10 is even, 4^{10} has units digit 6.
Therefore the rightmost digit (units digit) of the product is 6.