Highest Common Factor of 685, 53813 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 685, 53813 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 685, 53813 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 685, 53813 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 685, 53813 is 1.
HCF(685, 53813) = 1
HCF of 685, 53813 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 685, 53813 is 1.
Highest Common Factor of 685,53813 is 1
Step 1: Since 53813 > 685, we apply the division lemma to 53813 and 685, to get
53813 = 685 x 78 + 383
Step 2: Since the reminder 685 ≠ 0, we apply division lemma to 383 and 685, to get
685 = 383 x 1 + 302
Step 3: We consider the new divisor 383 and the new remainder 302, and apply the division lemma to get
383 = 302 x 1 + 81
We consider the new divisor 302 and the new remainder 81,and apply the division lemma to get
302 = 81 x 3 + 59
We consider the new divisor 81 and the new remainder 59,and apply the division lemma to get
81 = 59 x 1 + 22
We consider the new divisor 59 and the new remainder 22,and apply the division lemma to get
59 = 22 x 2 + 15
We consider the new divisor 22 and the new remainder 15,and apply the division lemma to get
22 = 15 x 1 + 7
We consider the new divisor 15 and the new remainder 7,and apply the division lemma to get
15 = 7 x 2 + 1
We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 685 and 53813 is 1
Notice that 1 = HCF(7,1) = HCF(15,7) = HCF(22,15) = HCF(59,22) = HCF(81,59) = HCF(302,81) = HCF(383,302) = HCF(685,383) = HCF(53813,685) .
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Frequently Asked Questions on HCF of 685, 53813 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 685, 53813?
Answer: HCF of 685, 53813 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 685, 53813 using Euclid's Algorithm?
Answer: For arbitrary numbers 685, 53813 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
