Factors and multiples

Weekly Problem 22 - 2008
The following sequence continues indefinitely... Which of these integers is a multiple of 81?

The sum of 9 consecutive positive whole numbers is 2007. What is the largest of these numbers?

Ben and his mum are planting garlic. Can you find out how many cloves of garlic they might have had?

Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?

This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?

Can you complete this jigsaw of the multiplication square?

Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?

If you count from 1 to 20 and clap more loudly on the numbers in the two times table, as well as saying those numbers loudly, which numbers will be loud?

Show that it is rare for a ratio of ratios to be rational.

Using your knowledge of the properties of numbers, can you fill all the squares on the board?