Is there an efficient way to work out how many factors a large number has?
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?
Helen made the conjecture that "every multiple of six has more
factors than the two numbers either side of it". Is this conjecture
Jack and Zaim from London sent us this very clear explanation of why this happens.
Curtis from Shatin College used a similar strategy :
I divided all of the numbers by 11 and wrote down their remainders. Then I wrote a chart of them, in the same spot. After that, I checked in the remainder box for any pairs that added up to 11. Finally I transfered the numbers back on to the provided grid, and came up with 28 solutions for both the 11's and the 13's.
Adil from Valentines High School discovered the same property of the numbers that could be paired: