Other tags that relate to Factorial
Divisibility. Working systematically. Mathematical reasoning & proof. Factorials. Properties of numbers. Number - generally. Factors and multiples. Place value. Addition & subtraction. Multiplication & division.There are 95 results
Broad Topics > Numbers and the Number System > Factors and multiples
Factorial
Age 14 to 16 Challenge Level:
How many zeros are there at the end of the number which is the product of first hundred positive integers?
Times Right
Age 11 to 16 Challenge Level:
Using the digits 1, 2, 3, 4, 5, 6, 7 and 8, mulitply a two two digit numbers are multiplied to give a four digit number, so that the expression is correct. How many different solutions can you find?
Fac-finding
Age 14 to 16 Challenge Level:
Lyndon chose this as one of his favourite problems. It is accessible but needs some careful analysis of what is included and what is not. A systematic approach is really helpful.
Powerful Factorial
Age 11 to 14 Challenge Level:
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!?
Factoring Factorials
Age 11 to 14 Challenge Level:
Find the highest power of 11 that will divide into 1000! exactly.
Repeaters
Age 11 to 14 Challenge Level:
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.
A First Product Sudoku
Age 11 to 14 Challenge Level:
Given the products of adjacent cells, can you complete this Sudoku?
Big Powers
Age 11 to 16 Challenge Level:
Three people chose this as a favourite problem. It is the sort of problem that needs thinking time - but once the connection is made it gives access to many similar ideas.
Just Repeat
Age 11 to 14 Challenge Level:
Think of any three-digit number. Repeat the digits. The 6-digit number that you end up with is divisible by 91. Is this a coincidence?
Remainders
Age 7 to 14 Challenge Level:
I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?
Adding in Rows
Age 11 to 14 Challenge Level:
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?
American Billions
Age 11 to 14 Challenge Level:
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...
Counting Factors
Age 11 to 14 Challenge Level:
Is there an efficient way to work out how many factors a large number has?
Multiplication Magic
Age 14 to 16 Challenge Level:
Given any 3 digit number you can use the given digits and name another number which is divisible by 37 (e.g. given 628 you say 628371 is divisible by 37 because you know that 6+3 = 2+7 = 8+1 = 9). . . .
Adding All Nine
Age 11 to 14 Challenge Level:
Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some. . . .
Remainder
Age 11 to 14 Challenge Level:
What is the remainder when 2^2002 is divided by 7? What happens with different powers of 2?
Eminit
Age 11 to 14 Challenge Level:
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?
X Marks the Spot
Age 11 to 14 Challenge Level:
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" .
Thirty Six Exactly
Age 11 to 14 Challenge Level:
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
LCM Sudoku
Age 14 to 16 Challenge Level:
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
Counting Cogs
Age 7 to 14 Challenge Level:
Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?
Funny Factorisation
Age 11 to 16 Challenge Level:
Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?
Gaxinta
Age 11 to 14 Challenge Level:
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?
N000ughty Thoughts
Age 14 to 16 Challenge Level:
How many noughts are at the end of these giant numbers?
Gabriel's Problem
Age 11 to 14 Challenge Level:
Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
Squaresearch
Age 14 to 16 Challenge Level:
Consider numbers of the form un = 1! + 2! + 3! +...+n!. How many such numbers are perfect squares?
Transposition Cipher
Age 11 to 16 Challenge Level:
Can you work out what size grid you need to read our secret message?
Dozens
Age 7 to 14 Challenge Level:
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
Expenses
Age 14 to 16 Challenge Level:
What is the largest number which, when divided into 1905, 2587, 3951, 7020 and 8725 in turn, leaves the same remainder each time?
Digat
Age 11 to 14 Challenge Level:
What is the value of the digit A in the sum below: [3(230 + A)]^2 = 49280A
Oh! Hidden Inside?
Age 11 to 14 Challenge Level:
Find the number which has 8 divisors, such that the product of the divisors is 331776.
Factor Track
Age 7 to 14 Challenge Level:
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.
Two Much
Age 11 to 14 Challenge Level:
Explain why the arithmetic sequence 1, 14, 27, 40, ... contains many terms of the form 222...2 where only the digit 2 appears.
What a Joke
Age 14 to 16 Challenge Level:
Each letter represents a different positive digit AHHAAH / JOKE = HA What are the values of each of the letters?
Mathematical Swimmer
Age 11 to 14 Challenge Level:
Can you work out how many lengths I swim each day?
Phew I'm Factored
Age 14 to 16 Challenge Level:
Explore the factors of the numbers which are written as 10101 in different number bases. Prove that the numbers 10201, 11011 and 10101 are composite in any base.
Ben's Game
Age 11 to 16 Challenge Level:
Ben, Jack and Emma passed counters to each other and ended with the same number of counters. How many did they start with?
Flow Chart
Age 11 to 14 Challenge Level:
The flow chart requires two numbers, M and N. Select several values for M and try to establish what the flow chart does.
Can You Find a Perfect Number?
Age 7 to 14
Can you find any perfect numbers? Read this article to find out more...
Inclusion Exclusion
Age 11 to 14 Challenge Level:
How many integers between 1 and 1200 are NOT multiples of any of the numbers 2, 3 or 5?
One to Eight
Age 11 to 14 Challenge Level:
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.
Satisfying Statements
Age 11 to 14 Challenge Level:
Can you find any two-digit numbers that satisfy all of these statements?
Even So
Age 11 to 14 Challenge Level:
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?
A Biggy
Age 14 to 16 Challenge Level:
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 power.
Product Sudoku
Age 11 to 16 Challenge Level:
The clues for this Sudoku are the product of the numbers in adjacent squares.
Three Times Seven
Age 11 to 14 Challenge Level:
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
Factoring a Million
Age 14 to 16 Challenge Level:
In how many ways can the number 1 000 000 be expressed as the product of three positive integers?
Different by One
Age 14 to 16 Challenge Level:
Can you make lines of Cuisenaire rods that differ by 1?
Really Mr. Bond
Age 14 to 16 Challenge Level:
115^2 = (110 x 120) + 25, that is 13225 895^2 = (890 x 900) + 25, that is 801025 Can you explain what is happening and generalise?
What Numbers Can We Make Now?
Age 11 to 14 Challenge Level:
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
NRICH is part of the family of activities in the Millennium Mathematics Project.