Highest Common Factor of 423, 691, 297 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 423, 691, 297 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 423, 691, 297 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 423, 691, 297 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 423, 691, 297 is 1.
HCF(423, 691, 297) = 1
HCF of 423, 691, 297 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 423, 691, 297 is 1.
Highest Common Factor of 423,691,297 is 1
Step 1: Since 691 > 423, we apply the division lemma to 691 and 423, to get
691 = 423 x 1 + 268
Step 2: Since the reminder 423 ≠ 0, we apply division lemma to 268 and 423, to get
423 = 268 x 1 + 155
Step 3: We consider the new divisor 268 and the new remainder 155, and apply the division lemma to get
268 = 155 x 1 + 113
We consider the new divisor 155 and the new remainder 113,and apply the division lemma to get
155 = 113 x 1 + 42
We consider the new divisor 113 and the new remainder 42,and apply the division lemma to get
113 = 42 x 2 + 29
We consider the new divisor 42 and the new remainder 29,and apply the division lemma to get
42 = 29 x 1 + 13
We consider the new divisor 29 and the new remainder 13,and apply the division lemma to get
29 = 13 x 2 + 3
We consider the new divisor 13 and the new remainder 3,and apply the division lemma to get
13 = 3 x 4 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 423 and 691 is 1
Notice that 1 = HCF(3,1) = HCF(13,3) = HCF(29,13) = HCF(42,29) = HCF(113,42) = HCF(155,113) = HCF(268,155) = HCF(423,268) = HCF(691,423) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 297 > 1, we apply the division lemma to 297 and 1, to get
297 = 1 x 297 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 297 is 1
Notice that 1 = HCF(297,1) .
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Frequently Asked Questions on HCF of 423, 691, 297 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 423, 691, 297?
Answer: HCF of 423, 691, 297 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 423, 691, 297 using Euclid's Algorithm?
Answer: For arbitrary numbers 423, 691, 297 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.