Highest Common Factor of 854, 458, 495 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 854, 458, 495 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 854, 458, 495 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 854, 458, 495 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 854, 458, 495 is 1.

HCF(854, 458, 495) = 1

HCF of 854, 458, 495 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 854, 458, 495 is 1.

Highest Common Factor of 854,458,495 using Euclid's algorithm

Highest Common Factor of 854,458,495 is 1

Step 1: Since 854 > 458, we apply the division lemma to 854 and 458, to get

854 = 458 x 1 + 396

Step 2: Since the reminder 458 ≠ 0, we apply division lemma to 396 and 458, to get

458 = 396 x 1 + 62

Step 3: We consider the new divisor 396 and the new remainder 62, and apply the division lemma to get

396 = 62 x 6 + 24

We consider the new divisor 62 and the new remainder 24,and apply the division lemma to get

62 = 24 x 2 + 14

We consider the new divisor 24 and the new remainder 14,and apply the division lemma to get

24 = 14 x 1 + 10

We consider the new divisor 14 and the new remainder 10,and apply the division lemma to get

14 = 10 x 1 + 4

We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get

10 = 4 x 2 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 854 and 458 is 2

Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(14,10) = HCF(24,14) = HCF(62,24) = HCF(396,62) = HCF(458,396) = HCF(854,458) .

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

Step 1: Since 495 > 2, we apply the division lemma to 495 and 2, to get

495 = 2 x 247 + 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 495 is 1

Notice that 1 = HCF(2,1) = HCF(495,2) .

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Frequently Asked Questions on HCF of 854, 458, 495 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 854, 458, 495?

Answer: HCF of 854, 458, 495 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 854, 458, 495 using Euclid's Algorithm?

Answer: For arbitrary numbers 854, 458, 495 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.