Question

Find HCF by Euclid’s division algorithm of 96, 144, 225

Answer 1

Step-by-step explanation:

Given :-

96, 144, 225

To find:-

Find HCF by Euclid’s division algorithm?

Solution:-

Given numbers are 96, 144, 225

To find the HCF by using Euclid's Division Lemma first we have to find the HCF of any two numbers and then find the HCF of the other and the resulting answer.

Euclid's Division Lemma:-

For two positive integers a and b there exists integers q and r satisfying a=bq+r, 0≤r<b.

Finding HCF of 96 and 144:-

Let a = 144 and b = 96

On writing a = bq+r

=> 144 = 96×1+48

and Let a = 96 and b = 48

=> 96=48×2+0

HCF of 96 and 144 = 48

Finding HCF of 48 and 225:-

Let a = 225 and b = 48

On writing a = bq+r

=> 225 = 48×4+33

and Let a = 48 and b = 33

=> 48=33×1+15

and Let a = 33 and b= 15

33= 15×2+3

and Let a = 15 and b = 3

=> 15=3×5+0

HCF of 48 and 225 = 3

Answer:-

HCF of the numbers 96,144 and 225 is 3

Used formula:-

Euclid's Division Lemma:-

For two positive integers a and b there exists integers q and r satisfying a=bq+r, 0≤r<b.

Answer 2

Answer:

HCF of 96, 144,225 is 3

Step-by-step explanation:

euclid division algorithm

euclid division algorithm a = b q + r

144 = 96 × 1 + 48

96 = 48 × 2 + 0

now take 48, 225

225= 48× 4 + 33

48=33×1 + 15

33 = 15 × 2 + 3

15 = 3 ×5+0

remainder= 0

we stop the process

HCF of 96, 144,225 is 3