Sum(not div by 7) = Sum(all) - Sum(div by 7)
Now the sum of an AP is
Sn = n/2 (first + last)
where n is the number of terms
Sum(All) = 10000/2 (1 + 10000) = 50005000
Sum(div by 7) = (9996/7)/2 (7 + 9996) = 1428/2 (10003) = 7142142
Sum(not div by 7) = Sum(all) - Sum(div by 7)
= 50005000 - 7142142
= 42 862 858
10000 = 16 x 625
This is easiest to answer by summing all the numbers 1-10000 and subtracting the sum of the multiples of 7 (7, 14, 21, ..., 9996). The sum of a series is: S = (first + last) x number_of_terms / 2 For for 1-10000, the sum is: S1 = (1 + 10000) x 10000 / 2 = 10001 x 5000 = 50005000 For the multiples of 7 the sum is: S2 = (7 + 9996) x 1428 / 2 = 10003 x 714 = 7142142 So the sum of all integers not greater than 10000 that are not divisible by 7 is: S = S1 - S2 = 50005000 - 7142142 = 42,862,858
10000/3 is 3333.3recurring, so no, it is not divisible by 3
270421/10000 = 27.0421
Int(10000/3) = Int(3333.3) = 3333
It is 83667.
10000 = 16 x 625
625*16=10000625+16=641
Counting 10000, there are 17999.
One less than 10000.
This is easiest to answer by summing all the numbers 1-10000 and subtracting the sum of the multiples of 7 (7, 14, 21, ..., 9996). The sum of a series is: S = (first + last) x number_of_terms / 2 For for 1-10000, the sum is: S1 = (1 + 10000) x 10000 / 2 = 10001 x 5000 = 50005000 For the multiples of 7 the sum is: S2 = (7 + 9996) x 1428 / 2 = 10003 x 714 = 7142142 So the sum of all integers not greater than 10000 that are not divisible by 7 is: S = S1 - S2 = 50005000 - 7142142 = 42,862,858
No. If a number is divisible by three, the sum of its digits will be divisible by three. Obviously, the sum of the digits of 10000 is 1, and 1 is not divisible by 3, so 10000 is not divisible by 3.
10000/3 is 3333.3recurring, so no, it is not divisible by 3
9000 integers.
125
Let me first re-phrase your question: What is the number of (positive) integers less than 10000 (5 digits) and greater than 999 (3 digits)? The greatest 4 digit integer would be 9999. The greatest 3 digit integer would be 999. Let's do some subtraction: 9999 - 999 = 9000 This works because as we count up from 999, each positive integer encountered satisfies your requirements until reaching 10000.
10,000 is composite. It is divisible by 2.