How many 4-digit numbers are multiples of both 2 and 5?
To be a multiple of 2 and 5, it must be a multiple of 10, that is, it must end in a zero
so number of such numbers
= 9 x 10 x 10 x 1 = 900
tysm!
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To find the number of 4-digit numbers that are multiples of both 2 and 5, we need to find the common multiples of 2 and 5 within the range of 1000 to 9999.
We first need to find the multiples of 2 within this range. A number is a multiple of 2 if it is divisible by 2. The smallest 4-digit multiple of 2 is 1000, and the largest 4-digit multiple of 2 is 9998. Therefore, we have:
Number of multiples of 2 = ((9998 - 1000) / 2) + 1
Next, we need to find the multiples of 5 within this range. Similar to the previous step, a number is a multiple of 5 if it is divisible by 5. The smallest 4-digit multiple of 5 is 1000, and the largest 4-digit multiple of 5 is 9995. Therefore, we have:
Number of multiples of 5 = ((9995 - 1000) / 5) + 1
Now, we need to find the multiples that are common to both 2 and 5. This means finding the numbers that are multiples of both 2 and 5 (multiples of 10). Since 10 is a common multiple of both 2 and 5, we can simply count the number of 4-digit multiples of 10:
Number of multiples of 10 = ((9990 - 1000) / 10) + 1
Finally, we can calculate the number of 4-digit numbers that are multiples of both 2 and 5 by taking the minimum of the number of multiples of 2 and the number of multiples of 5:
Number of 4-digit numbers that are multiples of both 2 and 5 = min(Number of multiples of 2, Number of multiples of 5)
Putting it all together:
Number of 4-digit numbers that are multiples of both 2 and 5 = min(((9998 - 1000) / 2) + 1, ((9995 - 1000) / 5) + 1)