Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
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.
The five digit number A679B, in base ten, is divisible by 72. What
are the values of A and B?
A game that tests your understanding of remainders.
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?
The clues for this Sudoku are the product of the numbers in adjacent squares.
Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
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?
What is the smallest number of answers you need to reveal in order
to work out the missing headers?
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?
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?"
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. . . .
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!?
Find the highest power of 11 that will divide into 1000! exactly.
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. . . .
Can you find any perfect numbers? Read this article to find out more...
Can you find a way to identify times tables after they have been shifted up?
What is the remainder when 2^2002 is divided by 7? What happens
with different powers of 2?
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
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.
Helen made the conjecture that "every multiple of six has more
factors than the two numbers either side of it". Is this conjecture
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...
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?
What is the value of the digit A in the sum below: [3(230 + A)]^2 =
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?
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" .
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?
How many zeros are there at the end of the number which is the
product of first hundred positive integers?
Is there an efficient way to work out how many factors a large number has?
How many integers between 1 and 1200 are NOT multiples of any of
the numbers 2, 3 or 5?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
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?
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?
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
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
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. . . .
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?
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.
Which pairs of cogs let the coloured tooth touch every tooth on the
other cog? Which pairs do not let this happen? Why?
Follow this recipe for sieving numbers and see what interesting patterns emerge.
Choose any 3 digits and make a 6 digit number by repeating the 3
digits in the same order (e.g. 594594). Explain why whatever digits
you choose the number will always be divisible by 7, 11 and 13.
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?
Can you work out what size grid you need to read our secret message?
Substitution and Transposition all in one! How fiendish can these codes get?
How many noughts are at the end of these giant numbers?