Question

find the hcf of 75 and 105 by using division method​

Answer 1

Answer:

Below detailed show work will make you learn how to find HCF of 105,75 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(105,75).

Here 105 is greater than 75

Now, consider the largest number as 'a' from the given number ie., 105 and 75 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 105 > 75, we apply the division lemma to 105 and 75, to get

105 = 75 x 1 + 30

Step 2: Since the reminder 75 ≠ 0, we apply division lemma to 30 and 75, to get

75 = 30 x 2 + 15

Step 3: We consider the new divisor 30 and the new remainder 15, and apply the division lemma to get

30 = 15 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 105 and 75 is 15

Notice that 15 = HCF(30,15) = HCF(75,30) = HCF(105,75) .

Therefore, HCF of 105,75 using Euclid's division lemma is 15.