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#### Resources tagged with Prime factors similar to There's Always One Isn't There:

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##### Other tags that relate to There's Always One Isn't There
Investigations. Divisibility. Prime factors. Spreadsheets. chemistry. physics. engineering. Common factors. Factors and multiples. Maths Supporting SET.

### There are 14 results

Broad Topics > Numbers and the Number System > Prime factors

### 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.

### 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!?

### 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.

### 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?

### 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?

### 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.

### Factoring Factorials

##### Stage: 3 Challenge Level:

Find the highest power of 11 that will divide into 1000! exactly.

### 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.

### 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.

### 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.