Highest Common Factor of 648, 401, 267 using Euclid's algorithm

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 648, 401, 267 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 648, 401, 267 is 1 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 648, 401, 267 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 648, 401, 267 is 1.

HCF(648, 401, 267) = 1

HCF of 648, 401, 267 using Euclid's algorithm

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

HCF of:

Highest common factor (HCF) of 648, 401, 267 is 1.

Highest Common Factor of 648,401,267 using Euclid's algorithm

Highest Common Factor of 648,401,267 is 1

Step 1: Since 648 > 401, we apply the division lemma to 648 and 401, to get

648 = 401 x 1 + 247

Step 2: Since the reminder 401 ≠ 0, we apply division lemma to 247 and 401, to get

401 = 247 x 1 + 154

Step 3: We consider the new divisor 247 and the new remainder 154, and apply the division lemma to get

247 = 154 x 1 + 93

We consider the new divisor 154 and the new remainder 93,and apply the division lemma to get

154 = 93 x 1 + 61

We consider the new divisor 93 and the new remainder 61,and apply the division lemma to get

93 = 61 x 1 + 32

We consider the new divisor 61 and the new remainder 32,and apply the division lemma to get

61 = 32 x 1 + 29

We consider the new divisor 32 and the new remainder 29,and apply the division lemma to get

32 = 29 x 1 + 3

We consider the new divisor 29 and the new remainder 3,and apply the division lemma to get

29 = 3 x 9 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 648 and 401 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(29,3) = HCF(32,29) = HCF(61,32) = HCF(93,61) = HCF(154,93) = HCF(247,154) = HCF(401,247) = HCF(648,401) .

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

Step 1: Since 267 > 1, we apply the division lemma to 267 and 1, to get

267 = 1 x 267 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 267 is 1

Notice that 1 = HCF(267,1) .

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Frequently Asked Questions on HCF of 648, 401, 267 using Euclid's Algorithm

1. What is the Euclid division algorithm?

Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.

2. what is the HCF of 648, 401, 267?

Answer: HCF of 648, 401, 267 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 648, 401, 267 using Euclid's Algorithm?

Answer: For arbitrary numbers 648, 401, 267 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.