There are 544 positive integers less than 1,000 that are either divisible by two or by 11.
There are 130 positive integers less than 1,000 that are divisible by seven but not divisible by 11
666 integers.
To find the number of positive integers less than 1001 that are divisible by either 2 or 5, we use the principle of inclusion-exclusion. First, the count of integers divisible by 2 is ( \left\lfloor \frac{1000}{2} \right\rfloor = 500 ), and those divisible by 5 is ( \left\lfloor \frac{1000}{5} \right\rfloor = 200 ). The count of integers divisible by both 2 and 5 (i.e., by 10) is ( \left\lfloor \frac{1000}{10} \right\rfloor = 100 ). Thus, the total is ( 500 + 200 - 100 = 600 ). Therefore, there are 600 positive integers less than 1001 that are divisible by either 2 or 5.
130 numbers
To find how many positive integers less than or equal to 10,000 are divisible by 2, 5, or 10, we can use the principle of inclusion-exclusion. The count of integers divisible by each is: Divisible by 2: ( \frac{10000}{2} = 5000 ) Divisible by 5: ( \frac{10000}{5} = 2000 ) Divisible by 10: ( \frac{10000}{10} = 1000 ) Applying inclusion-exclusion, we have: [ 5000 + 2000 - 1000 = 6000 ] Thus, there are 6000 positive integers less than or equal to 10,000 that are divisible by 2, 5, or 10.
There are 130 positive integers less than 1,000 that are divisible by seven but not divisible by 11
666 integers.
There are 1,000 positive integers between 1,000 and 9,999, inclusive, that are divisible by nine.
To find the number of positive integers less than 1001 that are divisible by either 2 or 5, we use the principle of inclusion-exclusion. First, the count of integers divisible by 2 is ( \left\lfloor \frac{1000}{2} \right\rfloor = 500 ), and those divisible by 5 is ( \left\lfloor \frac{1000}{5} \right\rfloor = 200 ). The count of integers divisible by both 2 and 5 (i.e., by 10) is ( \left\lfloor \frac{1000}{10} \right\rfloor = 100 ). Thus, the total is ( 500 + 200 - 100 = 600 ). Therefore, there are 600 positive integers less than 1001 that are divisible by either 2 or 5.
130 numbers
332
334 of them.
To find how many positive integers less than or equal to 10,000 are divisible by 2, 5, or 10, we can use the principle of inclusion-exclusion. The count of integers divisible by each is: Divisible by 2: ( \frac{10000}{2} = 5000 ) Divisible by 5: ( \frac{10000}{5} = 2000 ) Divisible by 10: ( \frac{10000}{10} = 1000 ) Applying inclusion-exclusion, we have: [ 5000 + 2000 - 1000 = 6000 ] Thus, there are 6000 positive integers less than or equal to 10,000 that are divisible by 2, 5, or 10.
you can say that 2/10 of every 10 integers is divisible by 5, so multiplying 2/10 by 100, giving you 200/1000 total integers are divisible by 5. half of all integers are odd, so divide 200/1000 by 2 is 100/1000, so you can correctly state that 100 odd integers under 1000 are divisible by 5.
333 integers.
There are 90 integers less than 1,000 that are divisible by 11.
There are 2828 integers between 1000 and 9999.