Factors and multiples

When coins are put into piles of six 3 remain and in piles of eight 7 remain. How many remain when they are put into piles of 24?

Two numbers can be placed adjacent if one of them divides the other. Using only $1,...,10$, can you write the longest such list?

You can make a calculator count for you by any number you choose. You can count by ones to reach 24. You can count by twos to reach 24. What else can you count by to reach 24?

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.

Great Granddad is very proud of his telegram from the Queen congratulating him on his hundredth birthday and he has friends who are even older than he is... When was he born?

Katie and Will have some balloons. Will's balloon burst at exactly the same size as Katie's at the beginning of a puff. How many puffs had Will done before his balloon burst?

Find 180 to the power 59 (mod 391) to crack the code. To find the secret number with a calculator we work with small numbers like 59 and 391 but very big numbers are used in the real world for this.

In this problem we are looking at sets of parallel sticks that cross each other. What is the least number of crossings you can make? And the greatest?

Use cubes to continue making the numbers from 7 to 20. Are they sticks, rectangles or squares?

Can you find the chosen number from the grid using the clues?