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How many numbers less than 1000 are not divisible by 4?
From 1 (inclusive) to 1000(inclusive,) 750.
How many natural numbers less than 1000 will have exactly 3 factors?
11
What is the largest number less 1000 that is divisible by 8?
1000 ÷ 8 = 125 → largest less than 1000 divisible by 8 is 124 x 8 = 992
How many natural numbers below 660 are divisible by 5 and 11 but not by 3?
8 of the numbers less than 660 are divisible by 5 and 11 but not 3. All numbers divisible by 5 and 11 are multiples of their lcm; lcm(5, 11) = 55 All numbers divisibile by 5, 11 and 3 are multiples of their lcm; lcm(5, 11, 3) = 165 659 ÷ 55 = 11 54/55 → 11 numbers less than 660 are divisible by 5 and 11 659 ÷ 165 = 3 164/165 → 3 numbers less than 660 are divisible by 5, 11 and 3 → of the 11 numbers less than 660 divisible by 5 and 11, 3 are also divisible by 3 → 11 - 3 = 8 numbers less than 660 are divisible by 5 and 11 but not 3,.
How many numbers less than 100 are divisible by 3 and 5?
The numbers that are divisible by both 3 and 5 have to be a factor of 15. That leaves 15, 30, 45, 60, 75, and 90. There are 6 numbers less than 100 divisible by 3 and 5
