Resources tagged with Prime factors similar to Divisibility Tests:
Other tags that relate to Divisibility Tests
Prime factors. Number theory. Mathematical induction. Factors and multiples. Combinatorics. Divisibility. Digital roots. Modulus arithmetic. Index notation/Indices. Mathematical reasoning & proof.There are 14 results
Broad Topics > Numbers and the Number System > Prime factors
Fac-finding
Stage: 4 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.
Factoring a Million
Stage: 4 Challenge Level:
In how many ways can the number 1 000 000 be expressed as the product of three positive integers?
Different by One
Stage: 4 Challenge Level:
Make a line of green and a line of yellow rods so that the lines differ in length by one (a white rod)
Powerful Factorial
Stage: 3 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!?
Thirty Six Exactly
Stage: 3 Challenge Level:
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
Flow Chart
Stage: 3 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.
A Biggy
Stage: 4 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.
Gaxinta
Stage: 3 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?
Factoring Factorials
Stage: 3 Challenge Level:
Find the highest power of 11 that will divide into 1000! exactly.
Why 24?
Stage: 4 Challenge Level:
Take any prime number greater than 3 , square it and subtract one. Working on the building blocks will help you to explain what is special about your results.
Just Repeat
Stage: 3 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?
One to Eight
Stage: 3 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.
There's Always One Isn't There
Stage: 4 Challenge Level:
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.
Great Granddad
Stage: 3 Challenge Level:
Great Granddad is very proud of his telegram from the Queen congratulating him on his hundredth birthday and he has friends who are even older than he is... When was he born?
NRICH is part of the family of activities in the Millennium Mathematics Project.