There are 8 primes between 35 and 70: 37, 41, 43, 47, 53, 59, 61, 67
All prime numbers are 6n ± 1 since:
6n is divisible by 6
6n + 2 = 2(3n + 1) which is divisible by 2
6n + 3 = 3(2n + 1) which is divisible by 3
leaving only 6n + 1 or 6n + 5 = 6(n+1) - 6 + 5 = 6k - 1 (where k = n-1) as possible primes.
The remainder when one of these is divided by 12 is:
If n is odd, let n = 2m + 1
→ possible prime = 6(2m+1) ± 1 = 12m + 6 ± 1
→ possible primes are 12m + 5 or 12m + 7
So the remainder is 5 or 7 which are both primes when divided by 12.
If n is even, let n = 2m
→ possible primes = 6n ± 1 = 6(2m) ± 1 = 12m ± 1
→ possible primes are 12m + 1 or 12(m-1)+12 - 1 = 12k + 11 (where k = m - 1)
So the remainder is 1 or 11, of which only 11 is prime, when divided by 12.
Thus all primes which are not of the form 12m + 1 (= 6n + 1 when n is even) have a remainder which is prime when divided by 12.
if m = 3, 12m + 1 = 37
If m = 4, 12m + 1 = 49 = 7² (not prime)
If m = 5, 12m + 1 = 61
so the primes to sum are: 41, 43, 47, 53, 59, 67 which gives:
41 + 43 + 47 + 53 + 59 + 67 = 310
This question is based on ignorance or misunderstanding. The sum of all the primes between 35 and 70 is a number which is divisible by 12 and so leaves no remainder when divided by 12. That is, the remainder is 0 and, as you should know, 0 is not a prime number.
An even number can be divided by 2 evenly. An odd number will have a remainder of 1 when divided by 2.
It is an Odd number. Even numbers are those which have no remainder when divided by 2.
1 can be divided into both numbers with no remainder
46 can be divided by these numbers without leaving a remainder: 1 2 23 and 46.
Odd numbers are those divided by two with remainder. Thus, between 5 and 8 there is be only one odd number 7.
An even number can be divided by 2 evenly. An odd number will have a remainder of 1 when divided by 2.
2521
It is an Odd number. Even numbers are those which have no remainder when divided by 2.
1 can be divided into both numbers with no remainder
A number between 1 and 500 is composite if it can be divided, without remainder, by a number other than 1 and itself.
factors& multiples
I don't think there is such a number.
46 can be divided by these numbers without leaving a remainder: 1 2 23 and 46.
37
There are 5 such numbers. The smallest is 63. The remaining numbers are 67, 71, 75, and 79
7, 37, 67, 97, 127, and an infinite number of other numbers in this series (starting with 7 and increasing in increments of 30) have a remainder of 1 when divided by 6 and a remainder of 2 when divided by 5.
There are no such numbers. Any number can be divided by SOME number without a remainder. For a start, you can divide any number except zero by itself, without a remainder. You can also divide any number by 1 - also, without a remainder.