Question

Activity to find the h.c.f. of two numbers experimentally based on euclid's division lemma or algorithm.

Answer 1

Answer:

Euclid's division lemma is a algorithm which find the h.c.f of two number.

There are any two integers a and b, there exists q and r such that it satisfies the given condition a = bq + r where 0 ≤ r < b. Let's learn more about it in this lesson.

Example to find hcf of two number:-

Let the two number are 320 and 132

Apply the Euclid’s Division Lemma,

step 1:-

• we will divide 320/132 then reminder will be 56.

• Divedend=diviser*quotient +reminder

i.e 320 = 132(2) + 56

step 2:-

• we will divide 132/56 then reminder will be 20.
• Divedend=diviser*quotient +reminder

i.e 132 = 56(2) + 20

step 3:-

• we will divide 56/20 then reminder will be 16.
• Divedend=diviser*quotient +reminder

i.e 56 = 20(2) + 16

step 4:-

• we will divide 20/16 then reminder will be 4.
• Divedend=diviser*quotient +reminder

i.e 20 = 16(1) + 4

step 5:-

• we will divide 20/16 then reminder will be 4.
• Divedend=diviser*quotient +reminder

i.e 16 = 4(4) + 0

• We have no remainder left.so, the second last remainder is the HCF, i.e the HCF of 320 and 132 is equal to 4.

⇒ HCF (320,132)= 4

#SPJ2

Answer 2

Euclid's division lemma is an algorithm that finds the h.c.f of two numbers.

There are two integers a and b, there exists q and r such that it satisfies the given condition a = bq + r where 0 ≤ r < b. Let's learn more about it in this lesson.

Example to find HCF of two numbers:-

Let the two numbers are 320 and 132

Apply the Euclid’s Division Lemma,

Step 1

We will divide 320/132 then the reminder will be 56.

Divedend=diviser*quotient +reminder

i.e 320 = 132(2) + 56

Step 2

We will divide 132/56 then the reminder will be 20.

Divedend=diviser*quotient +reminder

i.e 132 = 56(2) + 20

Step 3

We will divide 56/20 then the reminder will be 16.

Divedend=diviser*quotient +reminder

i.e 56 = 20(2) + 16

Step 4

We will divide 20/16 then the reminder will be 4.

Divedend=diviser*quotient +reminder

i.e 20 = 16(1) + 4

Step 5

We will divide 20/16 then the reminder will be 4.

Divedend=diviser*quotient +reminder

i.e 16 = 4(4) + 0

We have no remainder left. So, the second last remainder is the HCF, i.e the HCF of 320 and 132 is equal to 4.

⇒ HCF (320,132)= 4

#SPJ3