All the even numbers from 2 to 98 inclusive, except those ending in
0, are multiplied together. What is the rightmost digit, that is,
the units digit of the product?
(a) 0 (b) 2 (c) 4 (d) 6 (e) 8
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im confused on how to go about the problem. that's y i need help on how to start.
To determine the units digit of the product, we need to multiply all the even numbers from 2 to 98, except those ending in 0.
First, let's identify the numbers that we need to include in the product: 2, 4, 6, 8, 12, 14, ..., 96, 98.
We notice that every number in this sequence has a units digit of either 2, 4, 6, or 8. Numbers ending in 0 are excluded.
When we multiply numbers, the units digit of the product is determined by the units digits of the individual numbers. Multiplying any number by a number ending in 0 will always result in a number ending in 0.
Therefore, to find the rightmost digit of the product, we need to consider only the numbers 2, 4, 6, and 8.
When we multiply these numbers together, we get:
2 * 4 * 6 * 8 * 12 * 14 * ... * 96 * 98
Since multiplying any number by 2 results in an even number ending in 2, and multiplying any number by 4 results in an even number ending in 4, and so on, all the even multiples of 10 (20, 40, 60, 80) will not affect the rightmost digit of the product.
Therefore, we can exclude these four numbers and focus on the remaining numbers: 2, 4, 6, 8.
Multiplying these numbers together:
2 * 4 * 6 * 8
we get 384.
The units digit of 384 is 4.
Therefore, the rightmost digit, or the units digit, of the product is 4.
Therefore, the correct answer is (c) 4.