Highest Common Factor of 523, 854 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 523, 854 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 523, 854 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 523, 854 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 523, 854 is 1.
HCF(523, 854) = 1
HCF of 523, 854 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 523, 854 is 1.
Highest Common Factor of 523,854 is 1
Step 1: Since 854 > 523, we apply the division lemma to 854 and 523, to get
854 = 523 x 1 + 331
Step 2: Since the reminder 523 ≠ 0, we apply division lemma to 331 and 523, to get
523 = 331 x 1 + 192
Step 3: We consider the new divisor 331 and the new remainder 192, and apply the division lemma to get
331 = 192 x 1 + 139
We consider the new divisor 192 and the new remainder 139,and apply the division lemma to get
192 = 139 x 1 + 53
We consider the new divisor 139 and the new remainder 53,and apply the division lemma to get
139 = 53 x 2 + 33
We consider the new divisor 53 and the new remainder 33,and apply the division lemma to get
53 = 33 x 1 + 20
We consider the new divisor 33 and the new remainder 20,and apply the division lemma to get
33 = 20 x 1 + 13
We consider the new divisor 20 and the new remainder 13,and apply the division lemma to get
20 = 13 x 1 + 7
We consider the new divisor 13 and the new remainder 7,and apply the division lemma to get
13 = 7 x 1 + 6
We consider the new divisor 7 and the new remainder 6,and apply the division lemma to get
7 = 6 x 1 + 1
We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 523 and 854 is 1
Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(13,7) = HCF(20,13) = HCF(33,20) = HCF(53,33) = HCF(139,53) = HCF(192,139) = HCF(331,192) = HCF(523,331) = HCF(854,523) .
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Frequently Asked Questions on HCF of 523, 854 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 523, 854?
Answer: HCF of 523, 854 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 523, 854 using Euclid's Algorithm?
Answer: For arbitrary numbers 523, 854 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.