Highest Common Factor of 85, 188, 454 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 85, 188, 454 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 85, 188, 454 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 85, 188, 454 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 85, 188, 454 is 1.

HCF(85, 188, 454) = 1

HCF of 85, 188, 454 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 85, 188, 454 is 1.

Highest Common Factor of 85,188,454 using Euclid's algorithm

Highest Common Factor of 85,188,454 is 1

Step 1: Since 188 > 85, we apply the division lemma to 188 and 85, to get

188 = 85 x 2 + 18

Step 2: Since the reminder 85 ≠ 0, we apply division lemma to 18 and 85, to get

85 = 18 x 4 + 13

Step 3: We consider the new divisor 18 and the new remainder 13, and apply the division lemma to get

18 = 13 x 1 + 5

We consider the new divisor 13 and the new remainder 5,and apply the division lemma to get

13 = 5 x 2 + 3

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

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 85 and 188 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(13,5) = HCF(18,13) = HCF(85,18) = HCF(188,85) .

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

Step 1: Since 454 > 1, we apply the division lemma to 454 and 1, to get

454 = 1 x 454 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 454 is 1

Notice that 1 = HCF(454,1) .

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Frequently Asked Questions on HCF of 85, 188, 454 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 85, 188, 454?

Answer: HCF of 85, 188, 454 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 85, 188, 454 using Euclid's Algorithm?

Answer: For arbitrary numbers 85, 188, 454 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.