Find the number which has 8 divisors, such that the product of the divisors is 331776.
The five digit number A679B, in base ten, is divisible by 72. What are the values of A and B?
Find the highest power of 11 that will divide into 1000! exactly.
List any 3 numbers. It is always possible to find a subset of adjacent numbers that add up to a multiple of 3. Can you explain why and prove it?
6! = 6 × 5 × 4 × 3 × 2 × 1. The highest power of 2 that divides exactly into 6! is 4 since (6!) / (2^4) = 45. What is the highest power of two that divides exactly into 100!?
What digit must replace the star to make the number a multiple of 11?
Can you reconstruct the long division calculation from the 'skeleton'?
How many noughts are at the end of these giant numbers?
Prove that if a^2+b^2 is a multiple of 3 then both a and b are multiples of 3.
The four digits 5, 6, 7 and 8 are put at random in the spaces of the number : 3 _ 1 _ 4 _ 0 _ 9 2 Calculate the probability that the answer will be a multiple of 396.
