Page 39 - Math 7

Operations on Whole Numbers

Here, the greatest capacity of the vessel is the H.C.F. of 45 l, 60 l and 120 l.

45 60 1 15 120 8
-45 - 120
15 45 3 0
-45
0
? H.C.F. = 15
Hence, the required vessel with the greatest capacity is 15 l.

Example 5: What is the greatest number of students to whom 84 books, 140
exercise books, and 252 pens can be distributed equally? Also, find
the shares of each item among them.
Solution:
Here, the required greatest number of students is the H.C.F. of 84, 140 and 252.

2 84 2 140 2 252
2 42 2 70 2 126
3 21 5 35 3 63
3 21
7 7 7
Now, 184 = 2 u 2 u 3 u 7
140 = 2 u 2 u 5 u 7
252 = 2 u 2 u 3 u 3 u 7
?H.C.F. = 2 u 2 u 7 = 28
Again, to find the shares of each item,
84 ÷ 28 = 3, 140 ÷ 28 = 5, and 252 ÷ 28 = 9
Hence, the required greatest number of student is 28 and each student shares
3 books, 5 exercise books, and 9 pens.

EXERCISE 3.1

General Section - Classwork

1. Between 2 and 4, 2 is a factor of 4. So, 2 is the H.C.F. of 2 and 4.
Between 6 and 18, 6 is a factor of 18. So, 6 is the H.C.F of 6 and 18.
Let's investigate the idea from the above facts. Then say and write the H.C. F.
of the following pairs of numbers.
(a) 3 and 6 is ............. (b) 7 and 28 is ............. (c) 6 and 30 is .............

(d) 9 and 63 is ............. (e) 12 and 48 is ............. (f) 15 and 90 is .............

2. Let's take any two numbers 12 and 18.
The smaller number 12 = 2 × 6
6 can also divide 18 exactly. So, the H.C.F of 12 and 18 is 6.

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 37 Vedanta Excel in Mathematics - Book 7