Highest Common Factor of 214, 792, 361 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 214, 792, 361 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 214, 792, 361 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 214, 792, 361 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 214, 792, 361 is 1.

HCF(214, 792, 361) = 1

HCF of 214, 792, 361 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 214, 792, 361 is 1.

Highest Common Factor of 214,792,361 using Euclid's algorithm

Highest Common Factor of 214,792,361 is 1

Step 1: Since 792 > 214, we apply the division lemma to 792 and 214, to get

792 = 214 x 3 + 150

Step 2: Since the reminder 214 ≠ 0, we apply division lemma to 150 and 214, to get

214 = 150 x 1 + 64

Step 3: We consider the new divisor 150 and the new remainder 64, and apply the division lemma to get

150 = 64 x 2 + 22

We consider the new divisor 64 and the new remainder 22,and apply the division lemma to get

64 = 22 x 2 + 20

We consider the new divisor 22 and the new remainder 20,and apply the division lemma to get

22 = 20 x 1 + 2

We consider the new divisor 20 and the new remainder 2,and apply the division lemma to get

20 = 2 x 10 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 214 and 792 is 2

Notice that 2 = HCF(20,2) = HCF(22,20) = HCF(64,22) = HCF(150,64) = HCF(214,150) = HCF(792,214) .

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

Step 1: Since 361 > 2, we apply the division lemma to 361 and 2, to get

361 = 2 x 180 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 361 is 1

Notice that 1 = HCF(2,1) = HCF(361,2) .

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Frequently Asked Questions on HCF of 214, 792, 361 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 214, 792, 361?

Answer: HCF of 214, 792, 361 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 214, 792, 361 using Euclid's Algorithm?

Answer: For arbitrary numbers 214, 792, 361 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.