Playing with Numbers
ICSE Class 6 · Mathematics · Chapter 9
What this chapter covers
- Simplification of brackets
- Factors and multiples
- Even and odd numbers
- Divisibility rules
- Prime, composite and co-prime numbers
- Every number as a product of primes
Key definitions
Simplifying means working out a long expression step by step until only one number is left.
Brackets are signs placed around part of a sum to show which part is done before the rest.
An even number is a whole number that is a multiple of 2.
An odd number is a whole number that is not a multiple of 2.
A divisibility rule is a quick test that shows whether one number divides another exactly, without doing the full division.
A prime number is a number greater than 1 that has exactly two factors, 1 and the number itself.
A composite number is a number greater than 1 that has more than two factors.
Co-prime numbers are two numbers whose only common factor is 1.
Prime factorisation is the writing of a number as a product of its prime factors.
Key points
- Simplify brackets from the inside out: round ( ), then curly { }, then square [ ].
- After brackets, do "of", then division and multiplication from left to right, then addition and subtraction from left to right.
- A factor divides a number exactly; a multiple comes from multiplying the number by 1, 2, 3 and so on.
- A number has a limited list of factors but endless multiples.
- Even numbers end in 0, 2, 4, 6 or 8; odd numbers end in 1, 3, 5, 7 or 9.
- Divisibility rules let you test for 2, 3, 4, 5, 6, 8, 9, 10 and 11 without dividing.
- A prime number has exactly two factors; a composite number has more than two; 1 is neither.
- 2 is the only even prime.
- Co-prime numbers are a pair whose only common factor is 1; they need not be prime.
- Every composite number can be written as a product of primes, by a factor tree or by repeated division.