You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
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.
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
A game that tests your understanding of remainders.
The five digit number A679B, in base ten, is divisible by 72. What
are the values of A and B?
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?
The clues for this Sudoku are the product of the numbers in adjacent squares.
Given the products of diagonally opposite cells - can you complete this Sudoku?
How many numbers less than 1000 are NOT divisible by either: a) 2
or 5; or b) 2, 5 or 7?
Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
What is the smallest number of answers you need to reveal in order
to work out the missing headers?
I'm thinking of a number. When my number is divided by 5 the
remainder is 4. When my number is divided by 3 the remainder is 2.
Can you find my number?
Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...
Some 4 digit numbers can be written as the product of a 3 digit
number and a 2 digit number using the digits 1 to 9 each once and
only once. The number 4396 can be written as just such a product.
Can. . . .
Can you find a way to identify times tables after they have been shifted up?
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!?
Twice a week I go swimming and swim the same number of lengths of the pool each time. As I swim, I count the lengths I've done so far, and make it into a fraction of the whole number of lengths I. . . .
When the number x 1 x x x is multiplied by 417 this gives the
answer 9 x x x 0 5 7. Find the missing digits, each of which is
represented by an "x" .
Find the highest power of 11 that will divide into 1000! exactly.
What is the remainder when 2^2002 is divided by 7? What happens
with different powers of 2?
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?"
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?
Can you find any perfect numbers? Read this article to find out more...
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
Find the number which has 8 divisors, such that the product of the
divisors is 331776.
What is the value of the digit A in the sum below: [3(230 + A)]^2 =
I put eggs into a basket in groups of 7 and noticed that I could
easily have divided them into piles of 2, 3, 4, 5 or 6 and always
have one left over. How many eggs were in the basket?
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
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?
Helen made the conjecture that "every multiple of six has more
factors than the two numbers either side of it". Is this conjecture
Is there an efficient way to work out how many factors a large number has?
How many zeros are there at the end of the number which is the
product of first hundred positive integers?
Make a line of green and a line of yellow rods so that the lines
differ in length by one (a white rod)
Given the products of adjacent cells, can you complete this Sudoku?
The sum of the first 'n' natural numbers is a 3 digit number in which all the digits are the same. How many numbers have been summed?
How many integers between 1 and 1200 are NOT multiples of any of
the numbers 2, 3 or 5?
How many noughts are at the end of these giant numbers?
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
Find some triples of whole numbers a, b and c such that a^2 + b^2 + c^2 is a multiple of 4. Is it necessarily the case that a, b and c must all be even? If so, can you explain why?
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.
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
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
This article takes the reader through divisibility tests and how they work. An article to read with pencil and paper to hand.
List any 3 numbers. It is always possible to find a subset of
adjacent numbers that add up to a multiple of 3. Can you explain
why and prove it?
Follow this recipe for sieving numbers and see what interesting patterns emerge.
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.
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.
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.
Using your knowledge of the properties of numbers, can you fill all the squares on the board?
What is the largest number which, when divided into 1905, 2587,
3951, 7020 and 8725 in turn, leaves the same remainder each time?