Highest Common Factor of 420, 562, 806 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 420, 562, 806 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 420, 562, 806 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 420, 562, 806 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 420, 562, 806 is 2.
HCF(420, 562, 806) = 2
HCF of 420, 562, 806 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 420, 562, 806 is 2.
Highest Common Factor of 420,562,806 is 2
Step 1: Since 562 > 420, we apply the division lemma to 562 and 420, to get
562 = 420 x 1 + 142
Step 2: Since the reminder 420 ≠ 0, we apply division lemma to 142 and 420, to get
420 = 142 x 2 + 136
Step 3: We consider the new divisor 142 and the new remainder 136, and apply the division lemma to get
142 = 136 x 1 + 6
We consider the new divisor 136 and the new remainder 6,and apply the division lemma to get
136 = 6 x 22 + 4
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 420 and 562 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(136,6) = HCF(142,136) = HCF(420,142) = HCF(562,420) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 806 > 2, we apply the division lemma to 806 and 2, to get
806 = 2 x 403 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 806 is 2
Notice that 2 = HCF(806,2) .
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Frequently Asked Questions on HCF of 420, 562, 806 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 420, 562, 806?
Answer: HCF of 420, 562, 806 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 420, 562, 806 using Euclid's Algorithm?
Answer: For arbitrary numbers 420, 562, 806 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.