Highest Common Factor of 430, 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 430, 734 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 430, 734 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 430, 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 430, 734 is 2.
HCF(430, 734) = 2
HCF of 430, 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 430, 734 is 2.
Highest Common Factor of 430,734 is 2
Step 1: Since 734 > 430, we apply the division lemma to 734 and 430, to get
734 = 430 x 1 + 304
Step 2: Since the reminder 430 ≠ 0, we apply division lemma to 304 and 430, to get
430 = 304 x 1 + 126
Step 3: We consider the new divisor 304 and the new remainder 126, and apply the division lemma to get
304 = 126 x 2 + 52
We consider the new divisor 126 and the new remainder 52,and apply the division lemma to get
126 = 52 x 2 + 22
We consider the new divisor 52 and the new remainder 22,and apply the division lemma to get
52 = 22 x 2 + 8
We consider the new divisor 22 and the new remainder 8,and apply the division lemma to get
22 = 8 x 2 + 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 430 and 734 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(22,8) = HCF(52,22) = HCF(126,52) = HCF(304,126) = HCF(430,304) = HCF(734,430) .
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Frequently Asked Questions on HCF of 430, 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 430, 734?
Answer: HCF of 430, 734 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 430, 734 using Euclid's Algorithm?
Answer: For arbitrary numbers 430, 734 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.