Activity to find the H.C.F of two numbers experimentally based on Euclid's division lemma or algorithm.

A simple activity to find HCF of two numbers experimentally based on Euclid’s division lemma is –

Required: Square sheet and maths kit.

Procedure: The steps are –

1. Cut one strip of length ‘a’ unit (say, a = 9 cm) and another strip of length ‘b’ unit (say, b = 5 cm) of width 1 cm each. Here, a > b.

2. Paste the strip of length ‘a’ unit above the strip of length ‘b’ unit aligned from the length from left, such that there will be length left. Let the remaining length be ‘c’ unit. (Here, (a – b) = c ⇒ (9 – 5) = 4 cm)

3. Cut another strip of length ‘b’ unit (here, b = 5 cm) and another strip of length ‘c’ unit (here, c = 4 cm).

4. Paste the strip of length ‘b’ unit above the strip of length ‘c’ unit aligned from the length from left, such that notice some lengths left out. Say, the remaining length has’ unit. (Here, (b – c) = d ⇒ (5 – 4) = 1 cm)

5. Repeat the process till the length proceeding strips covered completely and the second strip which covers the proceeding strips is the HCF of given number.

Here, we are following Euclid’s lemma.

Let a and b be any two positive integers. Then there exist two unique whole numbers q and r such that

a = b q + r,

where 0 ≤ r < b

Here, a is called the dividend,

b is called the divisor,

q is called the quotient and

r is called the remainder.