### 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?

### Rule of Three

If it takes four men one day to build a wall, how long does it take 60,000 men to build a similar wall?

# Largest Product

##### Stage: 3 Challenge Level:

Various sets of numbers add together to give a sum of $10$:

• $3 + 7 = 10$
• $2 + 8 = 10$
• $2.1 + 5.6 + 2.3 = 10$

The products of these sets are all different:

• $3 \times7 = 21$
• $2 \times 8 = 16$
• $2.1 \times 5.6 \times2.3 = 27.048$

What is the greatest product that can be made from numbers that add up to $10$?

Try using different starting numbers.

Can you find a strategy for splitting numbers so that you always get the largest product?