Factors and multiples

Which of the numbers shown is the product of exactly 3 distinct prime factors?

Can you sort numbers into sets? Can you give each set a name?

I am thinking of three sets of numbers less than 101. They are the red set, the green set and the blue set. Can you find all the numbers in the sets from these clues?

What could be the scores from five throws of this dice?

A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"

How many numbers less than 1000 are NOT divisible by either: a) 2 or 5; or b) 2, 5 or 7?

Weekly Problem 48 - 2013
What is the remainder when the number 743589×301647 is divided by 5?

I am thinking of three sets of numbers less than 101. Can you find all the numbers in each set from these clues?

Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.

115^2 = (110 x 120) + 25, that is 13225 895^2 = (890 x 900) + 25, that is 801025 Can you explain what is happening and generalise?