This document provides instructions for an activity to find the highest common factor (HCF) of two numbers experimentally based on Euclid's division lemma. The activity involves cutting strips of cardboard of different lengths to represent numbers, covering them in different colored paper, and arranging them according to the divisions in Euclid's lemma to visually demonstrate the HCF. Figures are provided to show how the strips should be arranged. The HCF is found to be the length of the final remaining strip. Observations of actual measurements are to be recorded to determine the HCF of the original two numbers.

1. ACTIVITY 01
CLASS X

2. OBJECTIVE
TO FIND THE HCF OF TWO
NUMBERS
EXPERIMENTALLY
BASED ON EUCLID’S
DIVISION LEMMA

3. MATERIALS REQUIRED
CARD BOARD SHEETS
GLAZED PAPERS OF DIFFERENT COLOURS
SCISSORS
RULER
SKETCH PEN
GLUE ETC.,

4. METHOD OF CONSTRUCTION
CUT OUT ONE STRIP OF LENGTH a UNITS, ONE
STRIP OF LENGTH b UNITS [ b<a], TWO STRIPS
EACH OF LENGTH c UNITS [ c<b], ONE STRIP OF
LENGTH d UNITS [ d<c] AND TWO STRIPS EACH
OF LENGTH e UNITS [ e<d] FROM THE
CARDBOARD.

5. METHOD OF CONSTRUCTION
COVER THESE STRIPS IN
DIFFERENT COLOURS USING
GLAZED PAPERS AS SHOWN IN
FIG 1 AND FIG 2.
a
b

6. FIGURES 3,4 & 5
C C
d
e e

7. Fig 6, 7, 8 and 9
STICK THESE STRIPS ON THE OTHER
CARDBOARD SHEET AS SHOWN IN THE
FIG.6 TO FIG.9
c
FIG.6
a
b
c

8. d
FIG 7.
FIG . 8 FIG. 9
b
c
c
c
d
d
e e
FIG CONTINUED…
d
e

9. DEMONSTRATION
AS PER EUCLID’S DIVISION LEMMA, [ a= bq + r]
FIG. 6 DEPICTS a = b X 1 + c
Here, q = 1, r = c
a
b
c

10. FIG.7 DEPICTS b = c X 2 + d
Here, q = 2 , r= d
b
c c
d

11. FIG.8 DEPICTS C = d X 1 + e
Here, q = 1 , r= e
FIG.8 DEPICTS d = e X 2 + 0
Here, q = 2 , r= 0
c
d e
d
e e

12. As per assumption in
Euclid Division Algorithm,
HCF of a and b = HCF of b and c
= HCF of c and d
= HCF of d and e
The HCF of d and e is equal to e.
So, HCF of a and b = e.

13. OBSERVATION
On actual measurement [ in mm ]
a = _____________, b = ________________
c = ______________, d = _________________
e = _______________
So, HCF of _________ and ________ = ________

14. CONCLUSION
The process depicted can be used for
Finding The HCF of two or more
numbers, which is Known as finding
HCF of numbers by Division Method.

15. THANK
U
FOR
LISTENING