Highest Common Factor of 678, 434 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 678, 434 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 678, 434 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 678, 434 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 678, 434 is 2.
HCF(678, 434) = 2
HCF of 678, 434 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 678, 434 is 2.
Highest Common Factor of 678,434 is 2
Step 1: Since 678 > 434, we apply the division lemma to 678 and 434, to get
678 = 434 x 1 + 244
Step 2: Since the reminder 434 ≠ 0, we apply division lemma to 244 and 434, to get
434 = 244 x 1 + 190
Step 3: We consider the new divisor 244 and the new remainder 190, and apply the division lemma to get
244 = 190 x 1 + 54
We consider the new divisor 190 and the new remainder 54,and apply the division lemma to get
190 = 54 x 3 + 28
We consider the new divisor 54 and the new remainder 28,and apply the division lemma to get
54 = 28 x 1 + 26
We consider the new divisor 28 and the new remainder 26,and apply the division lemma to get
28 = 26 x 1 + 2
We consider the new divisor 26 and the new remainder 2,and apply the division lemma to get
26 = 2 x 13 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 678 and 434 is 2
Notice that 2 = HCF(26,2) = HCF(28,26) = HCF(54,28) = HCF(190,54) = HCF(244,190) = HCF(434,244) = HCF(678,434) .
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Frequently Asked Questions on HCF of 678, 434 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 678, 434?
Answer: HCF of 678, 434 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 678, 434 using Euclid's Algorithm?
Answer: For arbitrary numbers 678, 434 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.