There are 25 prime numbers less than or equal to 100. What is the ones (units) digit of their product?

Question

There are 25 prime numbers less than or equal to 100. What is the ones (units) digit of their

product?

Answer 1

You could compile a list of those 25 prime numbers and multiply them all together (not fun). If you do compile the list you will see that 2 and 5 are the only prime numbers that do not end in 1, 3, 7, or 9. Any other integer then ends in an even number (0,2,4,6,8) or a 5 is not prime. If you multiply all those primes ending in 1,3,7, or 9, you will get some number. But you still have to multiply by 2 * 5 which is 10. But 10 times that big number that is the product of primes ending in (1,3,7,9) will result in a 1's digit of 0.