At 1, 2, 3 Of the 2000 natural numbers, there are______ Natural numbers can be divisible by 2 and 3 at the same time, and cannot be divisible by 5

At 1, 2, 3 Of the 2000 natural numbers, there are______ Natural numbers can be divisible by 2 and 3 at the same time, and cannot be divisible by 5

The number that can be divisible by 2 and 3 at the same time, that is, the number that can be divisible by 6 is 1, 2, 3 There are 6, 12, 18, 24 Let there be n such numbers, then: 1998 = 6 + (n-1) × 6, n = 333. Therefore, there are 333 numbers divisible by 2 and 3 at the same time. Among these 333 numbers, 30, 60, 90, 120 Suppose there are m such numbers, then 1980 = 30 + (m-1) × 30, M = 66, that is, there are 66 numbers divisible by 5. Therefore, there are 333-66 numbers divisible by 2 and 3 at the same time, and there are 267 numbers divisible by 5