Highest Common Factor of 610, 840, 216 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 610, 840, 216 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 610, 840, 216 is 2 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 610, 840, 216 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 610, 840, 216 is 2.
HCF(610, 840, 216) = 2
HCF of 610, 840, 216 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 610, 840, 216 is 2.
Highest Common Factor of 610,840,216 is 2
Step 1: Since 840 > 610, we apply the division lemma to 840 and 610, to get
840 = 610 x 1 + 230
Step 2: Since the reminder 610 ≠ 0, we apply division lemma to 230 and 610, to get
610 = 230 x 2 + 150
Step 3: We consider the new divisor 230 and the new remainder 150, and apply the division lemma to get
230 = 150 x 1 + 80
We consider the new divisor 150 and the new remainder 80,and apply the division lemma to get
150 = 80 x 1 + 70
We consider the new divisor 80 and the new remainder 70,and apply the division lemma to get
80 = 70 x 1 + 10
We consider the new divisor 70 and the new remainder 10,and apply the division lemma to get
70 = 10 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 610 and 840 is 10
Notice that 10 = HCF(70,10) = HCF(80,70) = HCF(150,80) = HCF(230,150) = HCF(610,230) = HCF(840,610) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 216 > 10, we apply the division lemma to 216 and 10, to get
216 = 10 x 21 + 6
Step 2: Since the reminder 10 ≠ 0, we apply division lemma to 6 and 10, to get
10 = 6 x 1 + 4
Step 3: We consider the new divisor 6 and the new remainder 4, and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2, and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 10 and 216 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(216,10) .
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Frequently Asked Questions on HCF of 610, 840, 216 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 610, 840, 216?
Answer: HCF of 610, 840, 216 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 610, 840, 216 using Euclid's Algorithm?
Answer: For arbitrary numbers 610, 840, 216 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.