An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
What is the smallest number with exactly 14 divisors?
Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?
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 you find the factors?
Maths is full of surprises! The number $5796$ can be written as a product like this in two DIFFERENT ways, and so can the number $5346$. Can you find these four funny factorisations?
Here is another puzzle, again you must use the digits $1$ to $9$ once, but only once, to replace the stars and complete this multiplication example.
This gives six funny factorisations, and there is one more.
You might like to write a computer program to find all seven funny factorisations, or you might come up with a different method.