Page 52 - ICSE Math 6

4 Playing with Numbers

Key Concepts

• Simplification of Brackets • Co-prime Numbers
• Factors and Multiples • Prime Factorization
• Types of Numbers (Even, Odd, Prime, Composite) • Highest Common Factor (HCF)
• Sieve of Eratosthenes • Lowest Common Multiple (LCM)
• Divisibility Tests of 2, 3, 4, 5, 6, 8, 9, 10 and 11 • Relation between HCF and LCM of Two Numbers
• Common Factors and Common Multiples

Simplification of Brackets

A bracket is a group of symbols which are used to separate a part of an expression. The difference
types of brackets are: bar, parenthesis, curly brackets, square brackets and angle brackets, and the
symbols for these brackets are: , ( ), { }, [ ], and < > respectively.
To simplify an expression containing one of the brackets, we first simplify the part inside the bracket.
For example, 5 + (3 –1) = 5 + 2 = 7
To simplify an expression containing two or more brackets one inside the other, we simplify the part
inside the innermost bracket first.
For example, 6 + {2 × (3 + 2)} = 6 + {2 × 5} = 6 + 10 = 16

Example 1: Simplify 45 – [30 – {18 + (2 × 9 ÷ 3)}].
___
Solution: 45 – [30 – {18 + (2 × 9 ÷ 3)}] = 45 – [30 – {18 + (2 × 3)}] Removing
= 45 – [30 – {18 + 6}] Removing ( )
= 45 – [30 – 24] Removing { }

= 45 – 6 Removing [ ]
= 39

Factors
Avinash wants to distribute 12 marbles equally among
his friends. Various Number of Marbles per
The table given alongside shows all the possible ways ways friend(s) friend
in which 12 marbles can be distributed equally. We (a) 1 12
observe that the numbers 1, 2, 3, 4, 6 and 12 divide 12
exactly and are therefore factors of 12. (b) 2 6
A factor is a number which divides a given number (c) 3 4
completely without leaving any remainder. We can also (d) 4 3
say that when two or more numbers are multiplied, then (e) 6 2
each number is a factor or divisor of the product. For (f) 12 1
example, 7 × 11 = 77. Therefore, 7 and 11 are factors
of 77.

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