Highest Common Factor of 66, 354, 467 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 66, 354, 467 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 66, 354, 467 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 66, 354, 467 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 66, 354, 467 is 1.

HCF(66, 354, 467) = 1

HCF of 66, 354, 467 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 66, 354, 467 is 1.

Highest Common Factor of 66,354,467 using Euclid's algorithm

Highest Common Factor of 66,354,467 is 1

Step 1: Since 354 > 66, we apply the division lemma to 354 and 66, to get

354 = 66 x 5 + 24

Step 2: Since the reminder 66 ≠ 0, we apply division lemma to 24 and 66, to get

66 = 24 x 2 + 18

Step 3: We consider the new divisor 24 and the new remainder 18, and apply the division lemma to get

24 = 18 x 1 + 6

We consider the new divisor 18 and the new remainder 6, and apply the division lemma to get

18 = 6 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 66 and 354 is 6

Notice that 6 = HCF(18,6) = HCF(24,18) = HCF(66,24) = HCF(354,66) .

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

Step 1: Since 467 > 6, we apply the division lemma to 467 and 6, to get

467 = 6 x 77 + 5

Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 5 and 6, to get

6 = 5 x 1 + 1

Step 3: We consider the new divisor 5 and the new remainder 1, and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 6 and 467 is 1

Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(467,6) .

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Frequently Asked Questions on HCF of 66, 354, 467 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 66, 354, 467?

Answer: HCF of 66, 354, 467 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 66, 354, 467 using Euclid's Algorithm?

Answer: For arbitrary numbers 66, 354, 467 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.