Highest Common Factor of 854, 669, 354 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, 669, 354 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 854, 669, 354 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, 669, 354 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, 669, 354 is 1.

HCF(854, 669, 354) = 1

HCF of 854, 669, 354 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, 669, 354 is 1.

Highest Common Factor of 854,669,354 using Euclid's algorithm

Highest Common Factor of 854,669,354 is 1

Step 1: Since 854 > 669, we apply the division lemma to 854 and 669, to get

854 = 669 x 1 + 185

Step 2: Since the reminder 669 ≠ 0, we apply division lemma to 185 and 669, to get

669 = 185 x 3 + 114

Step 3: We consider the new divisor 185 and the new remainder 114, and apply the division lemma to get

185 = 114 x 1 + 71

We consider the new divisor 114 and the new remainder 71,and apply the division lemma to get

114 = 71 x 1 + 43

We consider the new divisor 71 and the new remainder 43,and apply the division lemma to get

71 = 43 x 1 + 28

We consider the new divisor 43 and the new remainder 28,and apply the division lemma to get

43 = 28 x 1 + 15

We consider the new divisor 28 and the new remainder 15,and apply the division lemma to get

28 = 15 x 1 + 13

We consider the new divisor 15 and the new remainder 13,and apply the division lemma to get

15 = 13 x 1 + 2

We consider the new divisor 13 and the new remainder 2,and apply the division lemma to get

13 = 2 x 6 + 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 854 and 669 is 1

Notice that 1 = HCF(2,1) = HCF(13,2) = HCF(15,13) = HCF(28,15) = HCF(43,28) = HCF(71,43) = HCF(114,71) = HCF(185,114) = HCF(669,185) = HCF(854,669) .

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

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

354 = 1 x 354 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 354 is 1

Notice that 1 = HCF(354,1) .

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Frequently Asked Questions on HCF of 854, 669, 354 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, 669, 354?

Answer: HCF of 854, 669, 354 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 854, 669, 354 using Euclid's Algorithm?

Answer: For arbitrary numbers 854, 669, 354 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.