Highest Common Factor of 814, 666, 574 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, 666, 574 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 814, 666, 574 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, 666, 574 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, 666, 574 is 2.
HCF(814, 666, 574) = 2
HCF of 814, 666, 574 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, 666, 574 is 2.
Highest Common Factor of 814,666,574 is 2
Step 1: Since 814 > 666, we apply the division lemma to 814 and 666, to get
814 = 666 x 1 + 148
Step 2: Since the reminder 666 ≠ 0, we apply division lemma to 148 and 666, to get
666 = 148 x 4 + 74
Step 3: We consider the new divisor 148 and the new remainder 74, and apply the division lemma to get
148 = 74 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 74, the HCF of 814 and 666 is 74
Notice that 74 = HCF(148,74) = HCF(666,148) = HCF(814,666) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 574 > 74, we apply the division lemma to 574 and 74, to get
574 = 74 x 7 + 56
Step 2: Since the reminder 74 ≠ 0, we apply division lemma to 56 and 74, to get
74 = 56 x 1 + 18
Step 3: We consider the new divisor 56 and the new remainder 18, and apply the division lemma to get
56 = 18 x 3 + 2
We consider the new divisor 18 and the new remainder 2, and apply the division lemma to get
18 = 2 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 74 and 574 is 2
Notice that 2 = HCF(18,2) = HCF(56,18) = HCF(74,56) = HCF(574,74) .
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Frequently Asked Questions on HCF of 814, 666, 574 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, 666, 574?
Answer: HCF of 814, 666, 574 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 814, 666, 574 using Euclid's Algorithm?
Answer: For arbitrary numbers 814, 666, 574 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.