Highest Common Factor of 856, 2109, 8322 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 856, 2109, 8322 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 856, 2109, 8322 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 856, 2109, 8322 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 856, 2109, 8322 is 1.
HCF(856, 2109, 8322) = 1
HCF of 856, 2109, 8322 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 856, 2109, 8322 is 1.
Highest Common Factor of 856,2109,8322 is 1
Step 1: Since 2109 > 856, we apply the division lemma to 2109 and 856, to get
2109 = 856 x 2 + 397
Step 2: Since the reminder 856 ≠ 0, we apply division lemma to 397 and 856, to get
856 = 397 x 2 + 62
Step 3: We consider the new divisor 397 and the new remainder 62, and apply the division lemma to get
397 = 62 x 6 + 25
We consider the new divisor 62 and the new remainder 25,and apply the division lemma to get
62 = 25 x 2 + 12
We consider the new divisor 25 and the new remainder 12,and apply the division lemma to get
25 = 12 x 2 + 1
We consider the new divisor 12 and the new remainder 1,and apply the division lemma to get
12 = 1 x 12 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 856 and 2109 is 1
Notice that 1 = HCF(12,1) = HCF(25,12) = HCF(62,25) = HCF(397,62) = HCF(856,397) = HCF(2109,856) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 8322 > 1, we apply the division lemma to 8322 and 1, to get
8322 = 1 x 8322 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 8322 is 1
Notice that 1 = HCF(8322,1) .
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Frequently Asked Questions on HCF of 856, 2109, 8322 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 856, 2109, 8322?
Answer: HCF of 856, 2109, 8322 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 856, 2109, 8322 using Euclid's Algorithm?
Answer: For arbitrary numbers 856, 2109, 8322 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.