Question

use Euclid's divison algarithm to find the HCF of 112 and 256​

Answer 1

Answer:

Step 1: Since 256 > 144, we apply the division lemma to 256 and 144, to get

256 = 144 x 1 + 112

Step 2: Since the reminder 144 ≠ 0, we apply division lemma to 112 and 144, to get

144 = 112 x 1 + 32

Step 3: We consider the new divisor 112 and the new remainder 32, and apply the division lemma to get

112 = 32 x 3 + 16

We consider the new divisor 32 and the new remainder 16, and apply the division lemma to get

32 = 16 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 16, the HCF of 256 and 144 is 16

Notice that 16 = HCF(32,16) = HCF(112,32) = HCF(144,112) = HCF(256,144) = HCF(112,256)

Step-by-step explanation:

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