Highest Common Factor of 856, 321, 328 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, 321, 328 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 856, 321, 328 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, 321, 328 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, 321, 328 is 1.
HCF(856, 321, 328) = 1
HCF of 856, 321, 328 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, 321, 328 is 1.
Highest Common Factor of 856,321,328 is 1
Step 1: Since 856 > 321, we apply the division lemma to 856 and 321, to get
856 = 321 x 2 + 214
Step 2: Since the reminder 321 ≠ 0, we apply division lemma to 214 and 321, to get
321 = 214 x 1 + 107
Step 3: We consider the new divisor 214 and the new remainder 107, and apply the division lemma to get
214 = 107 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 107, the HCF of 856 and 321 is 107
Notice that 107 = HCF(214,107) = HCF(321,214) = HCF(856,321) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 328 > 107, we apply the division lemma to 328 and 107, to get
328 = 107 x 3 + 7
Step 2: Since the reminder 107 ≠ 0, we apply division lemma to 7 and 107, to get
107 = 7 x 15 + 2
Step 3: We consider the new divisor 7 and the new remainder 2, and apply the division lemma to get
7 = 2 x 3 + 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 107 and 328 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(107,7) = HCF(328,107) .
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Frequently Asked Questions on HCF of 856, 321, 328 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, 321, 328?
Answer: HCF of 856, 321, 328 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 856, 321, 328 using Euclid's Algorithm?
Answer: For arbitrary numbers 856, 321, 328 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
