Highest Common Factor of 340, 610 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 340, 610 i.e. 10 the largest integer that leaves a remainder zero for all numbers.
HCF of 340, 610 is 10 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 340, 610 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 340, 610 is 10.
HCF(340, 610) = 10
HCF of 340, 610 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 340, 610 is 10.
Highest Common Factor of 340,610 is 10
Step 1: Since 610 > 340, we apply the division lemma to 610 and 340, to get
610 = 340 x 1 + 270
Step 2: Since the reminder 340 ≠ 0, we apply division lemma to 270 and 340, to get
340 = 270 x 1 + 70
Step 3: We consider the new divisor 270 and the new remainder 70, and apply the division lemma to get
270 = 70 x 3 + 60
We consider the new divisor 70 and the new remainder 60,and apply the division lemma to get
70 = 60 x 1 + 10
We consider the new divisor 60 and the new remainder 10,and apply the division lemma to get
60 = 10 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 340 and 610 is 10
Notice that 10 = HCF(60,10) = HCF(70,60) = HCF(270,70) = HCF(340,270) = HCF(610,340) .
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Frequently Asked Questions on HCF of 340, 610 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 340, 610?
Answer: HCF of 340, 610 is 10 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 340, 610 using Euclid's Algorithm?
Answer: For arbitrary numbers 340, 610 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.