Highest Common Factor of 514, 906 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 514, 906 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 514, 906 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 514, 906 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 514, 906 is 2.
HCF(514, 906) = 2
HCF of 514, 906 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 514, 906 is 2.
Highest Common Factor of 514,906 is 2
Step 1: Since 906 > 514, we apply the division lemma to 906 and 514, to get
906 = 514 x 1 + 392
Step 2: Since the reminder 514 ≠ 0, we apply division lemma to 392 and 514, to get
514 = 392 x 1 + 122
Step 3: We consider the new divisor 392 and the new remainder 122, and apply the division lemma to get
392 = 122 x 3 + 26
We consider the new divisor 122 and the new remainder 26,and apply the division lemma to get
122 = 26 x 4 + 18
We consider the new divisor 26 and the new remainder 18,and apply the division lemma to get
26 = 18 x 1 + 8
We consider the new divisor 18 and the new remainder 8,and apply the division lemma to get
18 = 8 x 2 + 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 514 and 906 is 2
Notice that 2 = HCF(8,2) = HCF(18,8) = HCF(26,18) = HCF(122,26) = HCF(392,122) = HCF(514,392) = HCF(906,514) .
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Frequently Asked Questions on HCF of 514, 906 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 514, 906?
Answer: HCF of 514, 906 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 514, 906 using Euclid's Algorithm?
Answer: For arbitrary numbers 514, 906 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.