Highest Common Factor of 686, 836, 506, 40 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 686, 836, 506, 40 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 686, 836, 506, 40 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 686, 836, 506, 40 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 686, 836, 506, 40 is 2.
HCF(686, 836, 506, 40) = 2
HCF of 686, 836, 506, 40 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 686, 836, 506, 40 is 2.
Highest Common Factor of 686,836,506,40 is 2
Step 1: Since 836 > 686, we apply the division lemma to 836 and 686, to get
836 = 686 x 1 + 150
Step 2: Since the reminder 686 ≠ 0, we apply division lemma to 150 and 686, to get
686 = 150 x 4 + 86
Step 3: We consider the new divisor 150 and the new remainder 86, and apply the division lemma to get
150 = 86 x 1 + 64
We consider the new divisor 86 and the new remainder 64,and apply the division lemma to get
86 = 64 x 1 + 22
We consider the new divisor 64 and the new remainder 22,and apply the division lemma to get
64 = 22 x 2 + 20
We consider the new divisor 22 and the new remainder 20,and apply the division lemma to get
22 = 20 x 1 + 2
We consider the new divisor 20 and the new remainder 2,and apply the division lemma to get
20 = 2 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 686 and 836 is 2
Notice that 2 = HCF(20,2) = HCF(22,20) = HCF(64,22) = HCF(86,64) = HCF(150,86) = HCF(686,150) = HCF(836,686) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 506 > 2, we apply the division lemma to 506 and 2, to get
506 = 2 x 253 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 506 is 2
Notice that 2 = HCF(506,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 40 > 2, we apply the division lemma to 40 and 2, to get
40 = 2 x 20 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 40 is 2
Notice that 2 = HCF(40,2) .
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Frequently Asked Questions on HCF of 686, 836, 506, 40 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 686, 836, 506, 40?
Answer: HCF of 686, 836, 506, 40 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 686, 836, 506, 40 using Euclid's Algorithm?
Answer: For arbitrary numbers 686, 836, 506, 40 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
