Question

1. Use Euclid’s division algorithm to find the HCF of:

i. 135 and 225

ii. 196 and 38220

iii. 867 and 225​

Answer 1

Answer:

⭐i. 135 and 225.

Step-by-step explanation:

=》As you can see, from the question 225 is greater than 135. Therefore, by Euclid’s division algorithm, we have,

225 = 135 × 1 + 90

Now,

remainder 90 ≠ 0, thus again using division lemma for 90, we get,

135 = 90 × 1 + 45

Again,

45 ≠ 0, repeating the above step for 45, we get,

90 = 45 × 2 + 0

The remainder is now zero, so our method stops here. Since, in the last step, the divisor is 45, therefore, HCF (225,135) = HCF (135, 90) = HCF (90, 45) = 45.

Hence,

the HCF of 225 and 135 is 45.

ii. 196 and 38220

In this given question,

38220>196, therefore the by applying Euclid’s division algorithm and taking 38220 as divisor, we get,

38220 = 196 × 195 + 0

We have already got the remainder as 0 here. Therefore,

HCF(196, 38220) = 196.

Hence,

the HCF of 196 and 38220 is 196.

iii. 867 and 225

As we know,

867 is greater than 225. Let us apply now Euclid’s division algorithm on 867, to get,

867 = 225 × 3 + 102

Remainder 102 ≠ 0, therefore taking 225 as divisor and applying the division lemma method, we get,

225 = 102 × 2 + 51

Remainder 102 ≠ 0, therefore taking 225 as divisor and applying the division lemma method, we get,

225 = 102 × 2 + 51

Again, 51 ≠ 0. Now 102 is the new divisor, so repeating the same step we get,

102 = 51 × 2 + 0

The remainder is now zero, so our procedure stops here. Since, in the last step, the divisor is 51, therefore, HCF (867,225) = HCF(225,102) = HCF(102,51) = 51.

Hence, the HCF of 867 and 225 is 51.

Answer 2

Answer:

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Step-by-step explanation:

By Euclid's division lemma,

225=135×1+90

r=90

135=90×1+45

r=45

90=45×2+0

So, H.C.F of 135 and 225 is 45

(ii) By Euclid's division lemma,

38220=196×195+0r=0

So, H.C.F of 38220 and 196 is 196

(iii) By Euclid's division lemma,

867=255×3+102

r=102

255=102×2+51

r=51

102=51×2+0

So, H.C.F of 867 and 255 is 51

The highest HCF among the three is 196.