Highest Common Factor of 804, 891, 170 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 804, 891, 170 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 804, 891, 170 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 804, 891, 170 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 804, 891, 170 is 1.

HCF(804, 891, 170) = 1

HCF of 804, 891, 170 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 804, 891, 170 is 1.

Highest Common Factor of 804,891,170 using Euclid's algorithm

Highest Common Factor of 804,891,170 is 1

Step 1: Since 891 > 804, we apply the division lemma to 891 and 804, to get

891 = 804 x 1 + 87

Step 2: Since the reminder 804 ≠ 0, we apply division lemma to 87 and 804, to get

804 = 87 x 9 + 21

Step 3: We consider the new divisor 87 and the new remainder 21, and apply the division lemma to get

87 = 21 x 4 + 3

We consider the new divisor 21 and the new remainder 3, and apply the division lemma to get

21 = 3 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 804 and 891 is 3

Notice that 3 = HCF(21,3) = HCF(87,21) = HCF(804,87) = HCF(891,804) .

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

Step 1: Since 170 > 3, we apply the division lemma to 170 and 3, to get

170 = 3 x 56 + 2

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get

3 = 2 x 1 + 1

Step 3: 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 3 and 170 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(170,3) .

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Frequently Asked Questions on HCF of 804, 891, 170 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 804, 891, 170?

Answer: HCF of 804, 891, 170 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 804, 891, 170 using Euclid's Algorithm?

Answer: For arbitrary numbers 804, 891, 170 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.