Highest Common Factor of 867, 345, 916 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 867, 345, 916 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 867, 345, 916 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 867, 345, 916 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 867, 345, 916 is 1.

HCF(867, 345, 916) = 1

HCF of 867, 345, 916 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 867, 345, 916 is 1.

Highest Common Factor of 867,345,916 using Euclid's algorithm

Highest Common Factor of 867,345,916 is 1

Step 1: Since 867 > 345, we apply the division lemma to 867 and 345, to get

867 = 345 x 2 + 177

Step 2: Since the reminder 345 ≠ 0, we apply division lemma to 177 and 345, to get

345 = 177 x 1 + 168

Step 3: We consider the new divisor 177 and the new remainder 168, and apply the division lemma to get

177 = 168 x 1 + 9

We consider the new divisor 168 and the new remainder 9,and apply the division lemma to get

168 = 9 x 18 + 6

We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get

9 = 6 x 1 + 3

We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get

6 = 3 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 867 and 345 is 3

Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(168,9) = HCF(177,168) = HCF(345,177) = HCF(867,345) .

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

Step 1: Since 916 > 3, we apply the division lemma to 916 and 3, to get

916 = 3 x 305 + 1

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 916 is 1

Notice that 1 = HCF(3,1) = HCF(916,3) .

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Frequently Asked Questions on HCF of 867, 345, 916 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 867, 345, 916?

Answer: HCF of 867, 345, 916 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 867, 345, 916 using Euclid's Algorithm?

Answer: For arbitrary numbers 867, 345, 916 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.