(i) Concept used:
To obtain the HCF of two positive integers, say c and d, with c > d,we follow the steps below:
Step 1:
Apply Euclid’s division lemma, to c and d.
So, we find whole numbers, q and r such that c = dq + r, 0 ≤ r < d.
Step 2:
If r = 0, d is the HCF of c and d. If r ≠ 0, apply the division lemma to d and r.
Step 3 :
Continue the process till the remainder is zero.
The divisor at this stage will be the required HCF.
Now, We know that,
= 225>135
Applying Euclid’s division algorithm:
(Dividend = Divisor × Quotient + Remainder)
225 = 135 ×1+90
Here remainder = 90,
So, Again Applying Euclid’s division algorithm
135 = 90×1+45
Here remainder = 45,
So, Again Applying Euclid’s division algorithm
90 = 45×2+0
Remainder = 0,
Hence,
HCF of (135, 225) = 45
(ii) Concept used:
To obtain the HCF of two positive integers, say c and d, with c > d,we follow the steps below:
Step 1:
Apply Euclid’s division lemma, to c and d.
So, we find whole numbers, q and r such that c = dq + r, 0 ≤ r < d.
Step 2 :
If r = 0, d is the HCF of c and d. If r ≠ 0, apply the division lemma to d and r.
Step 3 :
Continue the process till the remainder is zero.
The divisor at this stage will be the required HCF.
Now, We know that,
38220>196
So, Applying Euclid’s division algorithm
38220 = 196×195+0
(Dividend = Divisor × Quotient + Remainder)
Remainder = 0
Hence,
HCF of (196, 38220) = 196
(iii) Concept used:
To obtain the HCF of two positive integers, say c and d, with c > d,we follow the steps below:
Step 1:
Apply Euclid’s division lemma, to c and d. So, we find whole numbers, q and r such that c = dq + r, 0 ≤ r < d.
Step 2:
If r = 0, d is the HCF of c and d. If r ≠ 0, apply the division lemma to d and r.
Step 3:
Continue the process till the remainder is zero.
The divisor at this stage will be the required HCF.
Now, We know that,
867>255
So, Applying Euclid’s division algorithm
867 = 255×3+102
(Dividend = Divisor × Quotient + Remainder)
Remainder = 102
So, Again Applying Euclid’s division algorithm
255 = 102×2+51
Remainder = 51
So, Again Applying Euclid’s division algorithm
102 = 51×2+0
Remainder = 0
Hence,
(HCF of 867 and 255) = 51
