Highest Common Factor of 430, 706 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, 706 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 430, 706 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, 706 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, 706 is 2.
HCF(430, 706) = 2
HCF of 430, 706 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, 706 is 2.
Highest Common Factor of 430,706 is 2
Step 1: Since 706 > 430, we apply the division lemma to 706 and 430, to get
706 = 430 x 1 + 276
Step 2: Since the reminder 430 ≠ 0, we apply division lemma to 276 and 430, to get
430 = 276 x 1 + 154
Step 3: We consider the new divisor 276 and the new remainder 154, and apply the division lemma to get
276 = 154 x 1 + 122
We consider the new divisor 154 and the new remainder 122,and apply the division lemma to get
154 = 122 x 1 + 32
We consider the new divisor 122 and the new remainder 32,and apply the division lemma to get
122 = 32 x 3 + 26
We consider the new divisor 32 and the new remainder 26,and apply the division lemma to get
32 = 26 x 1 + 6
We consider the new divisor 26 and the new remainder 6,and apply the division lemma to get
26 = 6 x 4 + 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 706 is 2
Notice that 2 = HCF(6,2) = HCF(26,6) = HCF(32,26) = HCF(122,32) = HCF(154,122) = HCF(276,154) = HCF(430,276) = HCF(706,430) .
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Frequently Asked Questions on HCF of 430, 706 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, 706?
Answer: HCF of 430, 706 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 430, 706 using Euclid's Algorithm?
Answer: For arbitrary numbers 430, 706 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.