Highest Common Factor of 474, 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 474, 814 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 474, 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 474, 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 474, 814 is 2.
HCF(474, 814) = 2
HCF of 474, 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 474, 814 is 2.
Highest Common Factor of 474,814 is 2
Step 1: Since 814 > 474, we apply the division lemma to 814 and 474, to get
814 = 474 x 1 + 340
Step 2: Since the reminder 474 ≠ 0, we apply division lemma to 340 and 474, to get
474 = 340 x 1 + 134
Step 3: We consider the new divisor 340 and the new remainder 134, and apply the division lemma to get
340 = 134 x 2 + 72
We consider the new divisor 134 and the new remainder 72,and apply the division lemma to get
134 = 72 x 1 + 62
We consider the new divisor 72 and the new remainder 62,and apply the division lemma to get
72 = 62 x 1 + 10
We consider the new divisor 62 and the new remainder 10,and apply the division lemma to get
62 = 10 x 6 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 474 and 814 is 2
Notice that 2 = HCF(10,2) = HCF(62,10) = HCF(72,62) = HCF(134,72) = HCF(340,134) = HCF(474,340) = HCF(814,474) .
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Frequently Asked Questions on HCF of 474, 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 474, 814?
Answer: HCF of 474, 814 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 474, 814 using Euclid's Algorithm?
Answer: For arbitrary numbers 474, 814 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.