Real Numbers
(NCERT Ex 1.1)
1. Use Euclid’s division algorithm to find the HCF of :
(i) 135 and 225
(ii) 196 and 38220
(iii) 867 and 255
Answer:
(i) 135 and 225
Step 1 : Since 225 > 135, apply Euclid’s division lemma to 225 and 135 to get
225 = 135 × 1 + 90
Step 2: Since remainder 90 ≠ 0, we apply the division lemma to 135 and 90 to get
135 = 90 × 1 + 45
Step 3: Now the remainder r = 45 ≠ 0 so we apply Euclid’s division lemma to 90 and 45 to have
90 = 2 × 45 + 0
Step 4: The remainder has now become zero. Since the divisor at this stage is 45,
∴ HCF(135,225) =
45
(ii) 196 and 38220
Step 1: Since 38220 > 196, apply the division lemma to 38220 and 196 to get
38220 = 196 × 195 + 0
Step 2: Since remainder is zero, the process stops. Since the divisor at this stage is 196,
∴ HCF(38220, 196) =
196
(iii) 867 and 255
Step 1: Since 867 > 255, we apply the division lemma to 867 and 255 to get
867 = 255 × 3 + 102
Step 2: Since remainder 102 ≠ 0, we apply the division lemma to 255 and 102 to have
255 = 102 × 2 + 51
Step 3: Now the new divisor is 102 and new remainder is 51. Apply the division lemma to get
102 = 51 × 2 + 0
Step 4: Since the remainder is zero, the process stops. Since the divisor at this stage is 51,
∴ HCF(867, 255) = 51
