Factors and multiples

problem
Neighbours

Age

7 to 11

Challenge level

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?
problem
How old are the children?

Age

11 to 14

Challenge level

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?"
problem
Two much

Age

11 to 14

Challenge level

Explain why the arithmetic sequence 1, 14, 27, 40, ... contains many terms of the form 222...2 where only the digit 2 appears.
problem
Times right

Age

11 to 16

Challenge level

Using the digits 1, 2, 3, 4, 5, 6, 7 and 8, mulitply a two two digit numbers are multiplied to give a four digit number, so that the expression is correct. How many different solutions can you find?
problem
Special sums and products

Age

11 to 14

Challenge level

Find some examples of pairs of numbers such that their sum is a factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and 16 is a factor of 48.
problem
Inclusion exclusion

Age

11 to 14

Challenge level

How many integers between 1 and 1200 are NOT multiples of any of the numbers 2, 3 or 5?
problem
Thirty six exactly

Age

11 to 14

Challenge level

The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
problem
Gaxinta

Age

11 to 14

Challenge level

A number N is divisible by 10, 90, 98 and 882 but it is NOT divisible by 50 or 270 or 686 or 1764. It is also known that N is a factor of 9261000. What is N?
problem
Digat

Age

11 to 14

Challenge level

What is the value of the digit A in the sum below: [3(230 + A)]^2 = 49280A
problem
AB search

Age

11 to 14

Challenge level

The five digit number A679B, in base ten, is divisible by 72. What are the values of A and B?