Highest Common Factor of 423, 728, 734 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, 728, 734 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 423, 728, 734 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, 728, 734 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, 728, 734 is 1.
HCF(423, 728, 734) = 1
HCF of 423, 728, 734 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, 728, 734 is 1.
Highest Common Factor of 423,728,734 is 1
Step 1: Since 728 > 423, we apply the division lemma to 728 and 423, to get
728 = 423 x 1 + 305
Step 2: Since the reminder 423 ≠ 0, we apply division lemma to 305 and 423, to get
423 = 305 x 1 + 118
Step 3: We consider the new divisor 305 and the new remainder 118, and apply the division lemma to get
305 = 118 x 2 + 69
We consider the new divisor 118 and the new remainder 69,and apply the division lemma to get
118 = 69 x 1 + 49
We consider the new divisor 69 and the new remainder 49,and apply the division lemma to get
69 = 49 x 1 + 20
We consider the new divisor 49 and the new remainder 20,and apply the division lemma to get
49 = 20 x 2 + 9
We consider the new divisor 20 and the new remainder 9,and apply the division lemma to get
20 = 9 x 2 + 2
We consider the new divisor 9 and the new remainder 2,and apply the division lemma to get
9 = 2 x 4 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 423 and 728 is 1
Notice that 1 = HCF(2,1) = HCF(9,2) = HCF(20,9) = HCF(49,20) = HCF(69,49) = HCF(118,69) = HCF(305,118) = HCF(423,305) = HCF(728,423) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 734 > 1, we apply the division lemma to 734 and 1, to get
734 = 1 x 734 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 734 is 1
Notice that 1 = HCF(734,1) .
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Frequently Asked Questions on HCF of 423, 728, 734 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, 728, 734?
Answer: HCF of 423, 728, 734 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 423, 728, 734 using Euclid's Algorithm?
Answer: For arbitrary numbers 423, 728, 734 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.