Highest Common Factor of 814, 688, 478 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 814, 688, 478 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 814, 688, 478 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 814, 688, 478 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 814, 688, 478 is 2.
HCF(814, 688, 478) = 2
HCF of 814, 688, 478 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 814, 688, 478 is 2.
Highest Common Factor of 814,688,478 is 2
Step 1: Since 814 > 688, we apply the division lemma to 814 and 688, to get
814 = 688 x 1 + 126
Step 2: Since the reminder 688 ≠ 0, we apply division lemma to 126 and 688, to get
688 = 126 x 5 + 58
Step 3: We consider the new divisor 126 and the new remainder 58, and apply the division lemma to get
126 = 58 x 2 + 10
We consider the new divisor 58 and the new remainder 10,and apply the division lemma to get
58 = 10 x 5 + 8
We consider the new divisor 10 and the new remainder 8,and apply the division lemma to get
10 = 8 x 1 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 814 and 688 is 2
Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(58,10) = HCF(126,58) = HCF(688,126) = HCF(814,688) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 478 > 2, we apply the division lemma to 478 and 2, to get
478 = 2 x 239 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 478 is 2
Notice that 2 = HCF(478,2) .
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Frequently Asked Questions on HCF of 814, 688, 478 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 814, 688, 478?
Answer: HCF of 814, 688, 478 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 814, 688, 478 using Euclid's Algorithm?
Answer: For arbitrary numbers 814, 688, 478 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.