Highest Common Factor of 338, 821, 514 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 338, 821, 514 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 338, 821, 514 is 1 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 338, 821, 514 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 338, 821, 514 is 1.
HCF(338, 821, 514) = 1
HCF of 338, 821, 514 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 338, 821, 514 is 1.
Highest Common Factor of 338,821,514 is 1
Step 1: Since 821 > 338, we apply the division lemma to 821 and 338, to get
821 = 338 x 2 + 145
Step 2: Since the reminder 338 ≠ 0, we apply division lemma to 145 and 338, to get
338 = 145 x 2 + 48
Step 3: We consider the new divisor 145 and the new remainder 48, and apply the division lemma to get
145 = 48 x 3 + 1
We consider the new divisor 48 and the new remainder 1, and apply the division lemma to get
48 = 1 x 48 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 338 and 821 is 1
Notice that 1 = HCF(48,1) = HCF(145,48) = HCF(338,145) = HCF(821,338) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 514 > 1, we apply the division lemma to 514 and 1, to get
514 = 1 x 514 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 514 is 1
Notice that 1 = HCF(514,1) .
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Frequently Asked Questions on HCF of 338, 821, 514 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 338, 821, 514?
Answer: HCF of 338, 821, 514 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 338, 821, 514 using Euclid's Algorithm?
Answer: For arbitrary numbers 338, 821, 514 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.