Maths 3 Mark Question

Factor:A factor of a number is an e×act divisor of that number.
For e×ample, 4 e×actly divide 32. Therefore, 4 is a factor of 32.
Examples of factors are:
2 and 3 are factors of 6 because 2 × 3 = 6
2 and 4 are factors of 8 because 2 × 4 = 8
3 and 4 are factors of 12 because 3 × 4 = 12
3 and 5 are factors of 15 because 3 × 5 = 15

Length of the rectangular courtyard = 20m 16cm = 2,016cm
Breadth of the rectangular courtyard = 15m 60cm = 1,560cm
Least possible side of the square stones used to pave the rectangular courtyard = HCF of (2,016 and 1,560)
Prime factorization of 2,016 =2 × 2 × 2 × 2 × 2 × 3 × 3 × 7
Prime factorization of 1,560 = 2 × 2 × 2 × 3 × 5 × 13 HCF of (2,016, 1,560) = 2 × 2 × 2 × 3= 24
Least possible side of square stones used to pave the rectangular courtyard is 24 cm. Number of square stones used to pave the rectangular courtyard
= Area of rectangular courtyard Area of square stone = 2016cm × 1560cm (24cm) 2 = 5460 Thus, the least number of square stones used to pave the rectangular courtyard is 5,460.

Length of the room = 8m 25cm = 825cm
Breadth of the room = 6m 75cm = 675cm
Height of the room = 4m 50cm = 450cm
The longest rod will be given by the HCF of 825, 675 and 450.
Prime factorization of 825 = 3 × 5 × 5 × 11
Prime factorization of 675 = 3 × 3 × 3 × 5 × 5
Prime factorization of 450 = 2 × 3 × 3 × 5 × 5 Therefore, HCF of 825, 675 and 450 = 3 × 5 × 5 = 75
Thus, the required length of the longest rod is 75cm.