Question

find the HCF of 36, 48 and 72 using long division method​

Answer 1

Answer:

12

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Answer 2

Step-by-step explanation:

HCF of 36, 48, 72 is 12 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.

Consider we have numbers 36, 48, 72 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b

Highest common factor (HCF) of 36, 48, 72 is 12.

HCF(36, 48, 72) = 12

HCF of 36, 48, 72 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

HCF of two or more Numbers

HCF of:

36, 48, 72

Highest common factor (HCF) of 36, 48, 72 is 12.

Highest Common Factor of 36,48,72 using Euclid's algorithm

Step 1: Since 48 > 36, we apply the division lemma to 48 and 36, to get

48 = 36 x 1 + 12

Step 2: Since the reminder 36 ≠ 0, we apply division lemma to 12 and 36, to get

36 = 12 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 36 and 48 is 12

Notice that 12 = HCF(36,12) = HCF(48,36) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 72 > 12, we apply the division lemma to 72 and 12, to get

72 = 12 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 12 and 72 is 12

Notice that 12 = HCF(72,12) .