Page 40 - Math 7

Operations on Whole Numbers

Let's take other two numbers 36 and 45.
The smaller number 36 = 2 × 18 18 cannot divide 45 exactly.
= 3 × 12 12 cannot divide 45 exactly.
= 4 × 9 9 can also divide 45 exactly.
So, the H.C.F. of 36 and 45 is 9.
Let's investigate the idea from the above facts. Say and write the H.C.F. of the
following pairs of numbers.

a) 6 and 9 is .............. b) 10 and 15 is .............. c) 12 and 30 is ..............

d) 18 and 24 is .............. e) 24 and 32 is .............. f) 21 and 28 is ..............
Creative Section - A

3. Let's write the sets of all possible factors and the sets of common factors of
these pairs of numbers, then find their H.C.F.
a) 9, 12 b) 15, 18 c) 12, 16 d) 18, 24 e) 36, 48
4. Let's find the H.C.F. of the following numbers by factorisation method.

a) 18, 24 b) 40, 50 c) 54, 72 d) 24, 36, 42
e) 35, 56, 70 f) 30, 75, 90 g) 32, 64, 80 h) 96, 144, 216
5. Let's find the H.C.F. of the following numbers by division method.
a) 12, 18 b) 28, 32 c) 36, 42 d) 52, 65
e) 12, 15, 18 f) 30, 45, 60 g) 156, 221, 390 h) 360, 456, 696
Creative Section - B

6. a) Find the greatest number that divides 45, 60 and 75 without leaving a
remainder.

b) Find the greatest number by which 60, 90 and 120 are exactly divisible.
7. a) Three jars of milk contain 40 l, 50 l and 60 l of milk. Find the greatest
capacity of a vessel which can empty out each jar with the exact number of
fillings.
b) What is the maximum number of students to whom 48 apples, 60 bananas
and 96 guavas can be distributed equally? Also find the shares of each
fruit.
8. a) A rectangular floor is 20 feet long and 16 feet broad. If it is to be paved
with squared marbles of same size, find the greatest length of each squared
marble.
b) The length, breadth and height of a room are 9 m 80 cm, 8 m 40 cm and
4 m 20 cm respectively. Find the longest tape which can measure the
all three dimensions of the room exactly.
9. a) Shaswat distributed 54 snickers, 72 kit kats and 90 cadburies equally to his
classmates on the occasion of his birthday. What was the greatest number
of his classmates? How many chocolates of each type did every one get?

Vedanta Excel in Mathematics - Book 7 38 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur