MATHS WORKSHOP

Read And Learn

Ancient prime numbers

Ancient civilisations were fascinated by prime numbers. We can see evidence of this in the work of Eratosthenes, who was born nearly three hundred years before Christ. Well, that’s nothing! It turns out that even longer ago, about 20 000 years ago in Zaire, a primitive man carved some numbers on a bone.

We have no idea what they mean, but the ones on the picture are the prime numbers between 10 and 20! What do you think about that?

Investigate

Perfect numbers

According to the Pythagoreans, a number is perfect if it coincides with the sum of its own divisors. For example, let’s take 6. The divisors of 6 are 1, 2 and 3 (6 is a divisor of 6, but it is not a proper divisor).

1 + 2 + 3 = 6

• There is another perfect number between 25 and 30. Can you find it?

Amicable numbers

Pythagoras called two numbers amicable when the sum of the divisors of each one was the same. A B

Sum of the divisors of B

Sum of the divisors of A

• The number 220 is amicable with another number. Can you find it?

Sharpen Your Wits

Stickers

• Amelia has stuck a number of stickers in her album that is three times the number of duplicates she needs to swap. If she manages to swap all of her duplicates for new ones she would have stuck a number of stickers in the album that is three times the empty spaces, which are more than 15 but less than 20. How many stickers are in the collection?