Highest Common Factor of 814, 514, 896 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, 514, 896 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 814, 514, 896 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, 514, 896 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, 514, 896 is 2.
HCF(814, 514, 896) = 2
HCF of 814, 514, 896 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, 514, 896 is 2.
Highest Common Factor of 814,514,896 is 2
Step 1: Since 814 > 514, we apply the division lemma to 814 and 514, to get
814 = 514 x 1 + 300
Step 2: Since the reminder 514 ≠ 0, we apply division lemma to 300 and 514, to get
514 = 300 x 1 + 214
Step 3: We consider the new divisor 300 and the new remainder 214, and apply the division lemma to get
300 = 214 x 1 + 86
We consider the new divisor 214 and the new remainder 86,and apply the division lemma to get
214 = 86 x 2 + 42
We consider the new divisor 86 and the new remainder 42,and apply the division lemma to get
86 = 42 x 2 + 2
We consider the new divisor 42 and the new remainder 2,and apply the division lemma to get
42 = 2 x 21 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 814 and 514 is 2
Notice that 2 = HCF(42,2) = HCF(86,42) = HCF(214,86) = HCF(300,214) = HCF(514,300) = HCF(814,514) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 896 > 2, we apply the division lemma to 896 and 2, to get
896 = 2 x 448 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 896 is 2
Notice that 2 = HCF(896,2) .
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Frequently Asked Questions on HCF of 814, 514, 896 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, 514, 896?
Answer: HCF of 814, 514, 896 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 814, 514, 896 using Euclid's Algorithm?
Answer: For arbitrary numbers 814, 514, 896 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
