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Counting Factors

Is there an efficient way to work out how many factors a large number has?

Summing Consecutive Numbers

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

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?

Repetitiously

Age 11 to 14 Challenge Level:

The number looks very similar when you multiply it by $100$.

A little subtraction goes a long way!

Factors and multiples. Place value. Rational and irrational numbers. Equivalent fractions, decimals and percentages. Decimals. Properties of numbers. Creating and manipulating expressions and formulae. Multiplication & division. Patterned numbers. Integers.