**Highest Common Factors**

Highest common factor is the greatest number which will divide exactly into two or more numbers. For example 4 is the highest common factor (HCF) of 20 & 24.

i.e. 20 = 1, 2, (4), 5, 10, 20

24= 1, 2, 3, (4), 6, 8, 12, 24

**Class work**

Find the HCF of:

(1) 28 and 42

(2) 504 and 588

(3) Find the LCM of 84 & 210

**READING ASSIGNMENT**

New General Mathematics, UBE Edition, chapter 1, pages 20-21

Essential Mathematics by A J S Oluwasanmi, Chapter 1, Pages 1-4

## PERFECT SQUARES

A perfect square is a whole number whose square root is also a whole number .It is always possible to express a perfect square in factors with even indices.

9 = 3×3

25= 5×5

225 = 15×15

= 3x5x3x5

= 3^{2} x 5^{2}

9216 =96 ^{2}

=3^{2 }x 32 ^{2}

=3^{2} x 4^{2} X 8^{2 }

=3^{2}x2^{4} x2^{6 }

=3^{2} x2 ^{10}

**READING ASSIGNMENT**

New General Mathematics, UBE Edition, chapter 1, pages 20-21

Essential Mathematics by A J S Oluwasanmi, Chapter 1, pages 1-4

**WEEKEND ASSIGNMENT**

- The lowest common multiple of 4, 6 and 8 is (a) 24 (b) 48 (c) 12 (d) 40
- Find the smallest number by which 72 must be multiplied so that its products will give a perfect square (a) 3 (b) 2 (c) 1 (d) 5
- The lowest common multiple of 4, 6 and 8 is (a) 24 (b) 48 (c) 12 (d) 40
- The H.C.F. of 8, 24 and 36 is ___ (a) 6 (b) 4 (c) 18 (d) 20
- The L.C.M. of 12, 16 and 24 is ___ (a) 96 (b) 48 (c) 108 (d) 24

**THEORY **

- Find the smallest number by which 162 must be multiplied so that its product will give a perfect square.
- Find the HCF and L.C.M. of the following figures

30 & 42

64 & 210

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