Highest Common Factor of 906, 814 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 906, 814 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 906, 814 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 906, 814 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 906, 814 is 2.
HCF(906, 814) = 2
HCF of 906, 814 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 906, 814 is 2.
Highest Common Factor of 906,814 is 2
Step 1: Since 906 > 814, we apply the division lemma to 906 and 814, to get
906 = 814 x 1 + 92
Step 2: Since the reminder 814 ≠ 0, we apply division lemma to 92 and 814, to get
814 = 92 x 8 + 78
Step 3: We consider the new divisor 92 and the new remainder 78, and apply the division lemma to get
92 = 78 x 1 + 14
We consider the new divisor 78 and the new remainder 14,and apply the division lemma to get
78 = 14 x 5 + 8
We consider the new divisor 14 and the new remainder 8,and apply the division lemma to get
14 = 8 x 1 + 6
We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get
8 = 6 x 1 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 906 and 814 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(14,8) = HCF(78,14) = HCF(92,78) = HCF(814,92) = HCF(906,814) .
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Frequently Asked Questions on HCF of 906, 814 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 906, 814?
Answer: HCF of 906, 814 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 906, 814 using Euclid's Algorithm?
Answer: For arbitrary numbers 906, 814 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.