Other tags that relate to Factorial
Number - generally. Creating and manipulating expressions and formulae. Properties of numbers. Indices. Making and proving conjectures. Factors and multiples. Mathematical reasoning & proof. Factorials. Multiplication & division. Working systematically.There are 92 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?
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?
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?
Helen's Conjecture
Age 11 to 14 Challenge Level:
Helen made the conjecture that "every multiple of six has more factors than the two numbers either side of it". Is this conjecture true?
Diggits
Age 11 to 14 Challenge Level:
Can you find what the last two digits of the number $4^{1999}$ are?
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!?
Mathematical Swimmer
Age 11 to 14 Challenge Level:
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. . . .
Factoring Factorials
Age 11 to 14 Challenge Level:
Find the highest power of 11 that will divide into 1000! exactly.
Can You Find a Perfect Number?
Age 7 to 14
Can you find any perfect numbers? Read this article to find out more...
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?
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?
N000ughty Thoughts
Age 14 to 16 Challenge Level:
How many noughts are at the end of these giant numbers?
Counting Factors
Age 11 to 14 Challenge Level:
Is there an efficient way to work out how many factors a large number has?
Number Rules - OK
Age 14 to 16 Challenge Level:
Can you convince me of each of the following: If a square number is multiplied by a square number the product is ALWAYS a square number...
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" .
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?
Neighbourly Addition
Age 7 to 14 Challenge Level:
I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?
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.
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.
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?
Sixational
Age 14 to 18 Challenge Level:
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. . . .
A First Product Sudoku
Age 11 to 14 Challenge Level:
Given the products of adjacent cells, can you complete this Sudoku?
For What?
Age 14 to 16 Challenge Level:
Prove that if the integer n is divisible by 4 then it can be written as the difference of two squares.
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?
Squaresearch
Age 14 to 16 Challenge Level:
Consider numbers of the form un = 1! + 2! + 3! +...+n!. How many such numbers are perfect squares?
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?
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?
Ben's Game
Age 11 to 14 Challenge Level:
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.
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). . . .
Data Chunks
Age 14 to 16 Challenge Level:
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. . . .
Star Product Sudoku
Age 11 to 16 Challenge Level:
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.
LCM Sudoku II
Age 11 to 18 Challenge Level:
You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.
Common Divisor
Age 14 to 16 Challenge Level:
Find the largest integer which divides every member of the following sequence: 1^5-1, 2^5-2, 3^5-3, ... n^5-n.
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?
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.
Sieve of Eratosthenes
Age 11 to 14 Challenge Level:
Follow this recipe for sieving numbers and see what interesting patterns emerge.
Satisfying Statements
Age 11 to 14 Challenge Level:
Can you find any two-digit numbers that satisfy all of these statements?
Mod 3
Age 14 to 16 Challenge Level:
Prove that if a^2+b^2 is a multiple of 3 then both a and b are multiples of 3.
Hot Pursuit
Age 11 to 14 Challenge Level:
I added together the first 'n' positive integers and found that my answer was a 3 digit number in which all the digits were the same...
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?
Special Sums and Products
Age 11 to 14 Challenge Level:
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.
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.
How Old Are the Children?
Age 11 to 14 Challenge Level:
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?"
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?
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.
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.
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?
Divisively So
Age 11 to 14 Challenge Level:
How many numbers less than 1000 are NOT divisible by either: a) 2 or 5; or b) 2, 5 or 7?
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?
NRICH is part of the family of activities in the Millennium Mathematics Project.