Highest Common Factor of 857, 323, 138, 413 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 857, 323, 138, 413 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 857, 323, 138, 413 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 857, 323, 138, 413 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 857, 323, 138, 413 is 1.
HCF(857, 323, 138, 413) = 1
HCF of 857, 323, 138, 413 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 857, 323, 138, 413 is 1.
Highest Common Factor of 857,323,138,413 is 1
Step 1: Since 857 > 323, we apply the division lemma to 857 and 323, to get
857 = 323 x 2 + 211
Step 2: Since the reminder 323 ≠ 0, we apply division lemma to 211 and 323, to get
323 = 211 x 1 + 112
Step 3: We consider the new divisor 211 and the new remainder 112, and apply the division lemma to get
211 = 112 x 1 + 99
We consider the new divisor 112 and the new remainder 99,and apply the division lemma to get
112 = 99 x 1 + 13
We consider the new divisor 99 and the new remainder 13,and apply the division lemma to get
99 = 13 x 7 + 8
We consider the new divisor 13 and the new remainder 8,and apply the division lemma to get
13 = 8 x 1 + 5
We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get
8 = 5 x 1 + 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 857 and 323 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(13,8) = HCF(99,13) = HCF(112,99) = HCF(211,112) = HCF(323,211) = HCF(857,323) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 138 > 1, we apply the division lemma to 138 and 1, to get
138 = 1 x 138 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 138 is 1
Notice that 1 = HCF(138,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 413 > 1, we apply the division lemma to 413 and 1, to get
413 = 1 x 413 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 413 is 1
Notice that 1 = HCF(413,1) .
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Frequently Asked Questions on HCF of 857, 323, 138, 413 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 857, 323, 138, 413?
Answer: HCF of 857, 323, 138, 413 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 857, 323, 138, 413 using Euclid's Algorithm?
Answer: For arbitrary numbers 857, 323, 138, 413 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
