Highest Common Factor of 420, 322, 27 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 420, 322, 27 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 420, 322, 27 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 420, 322, 27 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 420, 322, 27 is 1.

HCF(420, 322, 27) = 1

HCF of 420, 322, 27 using Euclid's algorithm

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

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Highest common factor (HCF) of 420, 322, 27 is 1.

Highest Common Factor of 420,322,27 using Euclid's algorithm

Highest Common Factor of 420,322,27 is 1

Step 1: Since 420 > 322, we apply the division lemma to 420 and 322, to get

420 = 322 x 1 + 98

Step 2: Since the reminder 322 ≠ 0, we apply division lemma to 98 and 322, to get

322 = 98 x 3 + 28

Step 3: We consider the new divisor 98 and the new remainder 28, and apply the division lemma to get

98 = 28 x 3 + 14

We consider the new divisor 28 and the new remainder 14, and apply the division lemma to get

28 = 14 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 14, the HCF of 420 and 322 is 14

Notice that 14 = HCF(28,14) = HCF(98,28) = HCF(322,98) = HCF(420,322) .

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

Step 1: Since 27 > 14, we apply the division lemma to 27 and 14, to get

27 = 14 x 1 + 13

Step 2: Since the reminder 14 ≠ 0, we apply division lemma to 13 and 14, to get

14 = 13 x 1 + 1

Step 3: We consider the new divisor 13 and the new remainder 1, and apply the division lemma to get

13 = 1 x 13 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 14 and 27 is 1

Notice that 1 = HCF(13,1) = HCF(14,13) = HCF(27,14) .

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Frequently Asked Questions on HCF of 420, 322, 27 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 420, 322, 27?

Answer: HCF of 420, 322, 27 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 420, 322, 27 using Euclid's Algorithm?

Answer: For arbitrary numbers 420, 322, 27 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.