Mathematics: How many 3-digit numbers are multiples of 3, but are not multiples of 4?

16Step-by-step explanation:We must find integers x, y with the most amount of prime divisors, not necessarily distinct, such that x + 3y 1,000. Obviously, this is achieved when the divisor is the least prime 2. So, we must find integers n, m such that since , then n must be 9. For n=9 we find the greatest integer m such that and we find m=7 and , are the numbers we are looking for and the sum of their length is 9+7 = 16. So, 16 is the maximum possible sum of the length of x and the length...

How many 3-digit numbers are multiples of 3, but - id3315334069, YaGirlNeedaLearn

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struckedblazing

11.02.2022

Mathematics

Step-by-step explanation:

We must find integers x, y with the most amount of prime divisors, not necessarily distinct, such that x + 3y < 1,000.

Obviously, this is achieved when the divisor is the least prime 2. So, we must find integers n, m such that

$\large 2^n + 3*2^m < 1,000$

since $\large 2^10 = 1,024$ , then n must be 9. For n=9 we find the greatest integer m such that

$\large 2^9 + 3*2^m <1,000$

and we find m=7

and $\large x=2^9$ , $\large y=2^7$ are the numbers we are looking for and the sum of their length is 9+7 = 16.

So, 16 is the maximum possible sum of the length of x and the length of y.

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How many 3-digit numbers are multiples of 3, but are not multiples of 4?

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