1. Show that the following numbers are composites:a. 2950 b. 18632. Complete the factor tree:       3. Find the lowest common multiple of 16 and 24.4. Use repeated division to write as the product of prime factors in index form:a. 44 b. 504 c. 6935. A wedding cake is 54 cm x 78 cm. The bride and groom want it cut into square pieces of equal size.a. What is the biggest size the pieces could be?b. How many pieces of this size could be cut?"

Solution:

1. 2950 = 2 $\times$ 5 $\times$ 5 $\times$ 59;  1863 = 3 $\times$ 3 $\times$ 3 $\times$ 3 $\times$ 23

These numbers have three or more factors. Hence are composite numbers.

2. Factor tree 60 = 6 $\times$ 10

                             6 = 2 $\times$ 3

                             10 = 2 $\times$ 5

3. LCM of 16 and 24 

   16 = 2 $\times$ $\times$ 2 $\times$ 2;  24 = 2 $\times$ 2 $\times$ 2 $\times$ 3;

    LCM = 2 $\times$ 2 $\times$ 2 $\times$ 2 $\times$ 2 $\times$3 = 48

    LCM of 16 and 24 is 48

4. 44 = 2 $\times$ 2 $\times$ 11; 504 = 2 $\times$ 2 $\times$ 2 $\times$ 3 $\times$3 $\times$ 7

5. HCF of 54, 78;  54 = 2 $\times$ 3 $\times$ 3 $\times$ 3 ; 78 = 2 $\times$ 3 $\times$ 13

      HCF = 2 $\times$ 3 = 6

a) Biggest size = 6 cm $\times$ 6 cm

b) Number of pieces = $\frac{54 \times 78}{6 \times6}$ = $9 \times 13 = 117$

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Updated on: 10-Oct-2022

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