Is 35 a prime number?

The number #35# ends in a #5#, so it is divisible by #5# and being greater than #5# itself is composite:

#35 = 5 xx 7#

You can test for divisibility by the first few prime numbers like this:

2: If the number ends with an even digit, then it is itself even, that is divisible by #2#

3: If the sum of the digits of a number is divisible by #3# then the number is divisible by #3# (and vice versa). For example #51# has digit sum #5+1 = 6# which is divisible by #3#, so #51# is divisible by #3#.

5: If the last digit is #5# or #0#, then the number is divisible by #5#.

There are methods for larger prime numbers, but they get more complicated. Often it is just as easy to divide the number, not bothering to remember the quotient on the way, just the remainder.

For example, to check whether #color(red)(28)color(purple)(8)color(blue)(1)# is divisible by #11#, note that #color(red)(28) = 22 + color(purple)(6)#, then #color(purple)(68) = 66 + color(blue)(2)# then #color(blue)(21)# is not divisible by #11#. So #2881# is not divisible by #11# either.