Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

14 Divisors

What is the smallest number with exactly 14 divisors?

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?

Fangs

Stage: 3 Short Challenge Level:

Alternate angles BDF and DFG are equal, so lines BD and FG are parallel.
Therefore angle BCA = angle FGC = $80^{\circ}$ (corresponding angles).

Consider triangle ABC: $x + 70 + 80 = 180$ so $x=30$.

This problem is taken from the UKMT Mathematical Challenges.
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