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14 Divisors

What is the smallest number with exactly 14 divisors?

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Summing Consecutive Numbers

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?

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Helen's Conjecture

Helen made the conjecture that "every multiple of six has more factors than the two numbers either side of it". Is this conjecture true?

One to Eight

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Sue from CBEC Basingstoke sent the following explanation to the first question:

** X ** = 4876
If you write 4876 as a product of prime factors you get 2 x 2 x 23 x 53
From this you need to find two, two digit numbers that use the digits 2, 3, 5 and 9
This has to be 2 x 2 x 23 = 92 and 53

We also received correct solutions from Jenny, Greenian, Rachael, Jacqui and Sam, from The Mount School, and Debbie from Forres Academy. Well done to you all.

53 x 92 = 4876
62 x 87 = 5394

24 x 57 = 1368
58 x 64 = 3712
52 x 34 = 1768

We'd like to hear from anyone who would like to explain how they solved these problems.
We are always interested in the reasoning that has helped you reach your solutions.