How many zeros are there at the end of the number which is the
product of first hundred positive integers?
This article takes the reader through divisibility tests and how they work. An article to read with pencil and paper to hand.
6! = 6 x 5 x 4 x 3 x 2 x 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!?
In how many ways can the number 1 000 000 be expressed as the
product of three positive integers?
Find the highest power of 11 that will divide into 1000! exactly.
Make a line of green and a line of yellow rods so that the lines
differ in length by one (a white rod)
How many noughts are at the end of these giant numbers?
Find the smallest positive integer N such that N/2 is a perfect
cube, N/3 is a perfect fifth power and N/5 is a perfect seventh
Take any pair of numbers, say 9 and 14. Take the larger number,
fourteen, and count up in 14s. Then divide each of those values by
the 9, and look at the remainders.
A collection of resources to support work on Factors and Multiples at Secondary level.
Substitution and Transposition all in one! How fiendish can these codes get?
Complete the following expressions so that each one gives a four
digit number as the product of two two digit numbers and uses the
digits 1 to 8 once and only once.
Given the products of diagonally opposite cells - can you complete this Sudoku?
Can you work out what size grid you need to read our secret message?
The puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid.
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
Data is sent in chunks of two different sizes - a yellow chunk has
5 characters and a blue chunk has 9 characters. A data slot of size
31 cannot be exactly filled with a combination of yellow and. . . .
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
Follow this recipe for sieving numbers and see what interesting patterns emerge.
Explore the relationship between simple linear functions and their
Prove that if a^2+b^2 is a multiple of 3 then both a and b are multiples of 3.
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?
What is the largest number which, when divided into 1905, 2587,
3951, 7020 and 8725 in turn, leaves the same remainder each time?
Helen made the conjecture that "every multiple of six has more
factors than the two numbers either side of it". Is this conjecture
Consider numbers of the form un = 1! + 2! + 3! +...+n!. How many such numbers are perfect squares?
The nth term of a sequence is given by the formula n^3 + 11n . Find
the first four terms of the sequence given by this formula and the
first term of the sequence which is bigger than one million. . . .
Prove that if the integer n is divisible by 4 then it can be written as the difference of two squares.
Find the largest integer which divides every member of the
following sequence: 1^5-1, 2^5-2, 3^5-3, ... n^5-n.
Ben passed a third of his counters to Jack, Jack passed a quarter
of his counters to Emma and Emma passed a fifth of her counters to
Ben. After this they all had the same number of counters.
Using your knowledge of the properties of numbers, can you fill all the squares on the board?
Can you find a relationship between the number of dots on the
circle and the number of steps that will ensure that all points are
Have you seen this way of doing multiplication ?
The clues for this Sudoku are the product of the numbers in adjacent squares.
Each letter represents a different positive digit
AHHAAH / JOKE = HA
What are the values of each of the letters?
Find the number which has 8 divisors, such that the product of the
divisors is 331776.
The number 8888...88M9999...99 is divisible by 7 and it starts with
the digit 8 repeated 50 times and ends with the digit 9 repeated 50
times. What is the value of the digit M?
How many integers between 1 and 1200 are NOT multiples of any of
the numbers 2, 3 or 5?
Can you find any perfect numbers? Read this article to find out more...
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
Find a cuboid (with edges of integer values) that has a surface
area of exactly 100 square units. Is there more than one? Can you
find them all?
A game that tests your understanding of remainders.
Factor track is not a race but a game of skill. The idea is to go round the track in as few moves as possible, keeping to the rules.
What is the smallest number of answers you need to reveal in order
to work out the missing headers?
Can you explain the strategy for winning this game with any target?
Find the frequency distribution for ordinary English, and use it to help you crack the code.
Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?