Highest Common Factor of 685, 410 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, 410 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 685, 410 is 5 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, 410 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, 410 is 5.
HCF(685, 410) = 5
HCF of 685, 410 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, 410 is 5.
Highest Common Factor of 685,410 is 5
Step 1: Since 685 > 410, we apply the division lemma to 685 and 410, to get
685 = 410 x 1 + 275
Step 2: Since the reminder 410 ≠ 0, we apply division lemma to 275 and 410, to get
410 = 275 x 1 + 135
Step 3: We consider the new divisor 275 and the new remainder 135, and apply the division lemma to get
275 = 135 x 2 + 5
We consider the new divisor 135 and the new remainder 5, and apply the division lemma to get
135 = 5 x 27 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 685 and 410 is 5
Notice that 5 = HCF(135,5) = HCF(275,135) = HCF(410,275) = HCF(685,410) .
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Frequently Asked Questions on HCF of 685, 410 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, 410?
Answer: HCF of 685, 410 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 685, 410 using Euclid's Algorithm?
Answer: For arbitrary numbers 685, 410 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.