Highest Common Factor of 676, 419, 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 676, 419, 434 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 676, 419, 434 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 676, 419, 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 676, 419, 434 is 1.
HCF(676, 419, 434) = 1
HCF of 676, 419, 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 676, 419, 434 is 1.
Highest Common Factor of 676,419,434 is 1
Step 1: Since 676 > 419, we apply the division lemma to 676 and 419, to get
676 = 419 x 1 + 257
Step 2: Since the reminder 419 ≠ 0, we apply division lemma to 257 and 419, to get
419 = 257 x 1 + 162
Step 3: We consider the new divisor 257 and the new remainder 162, and apply the division lemma to get
257 = 162 x 1 + 95
We consider the new divisor 162 and the new remainder 95,and apply the division lemma to get
162 = 95 x 1 + 67
We consider the new divisor 95 and the new remainder 67,and apply the division lemma to get
95 = 67 x 1 + 28
We consider the new divisor 67 and the new remainder 28,and apply the division lemma to get
67 = 28 x 2 + 11
We consider the new divisor 28 and the new remainder 11,and apply the division lemma to get
28 = 11 x 2 + 6
We consider the new divisor 11 and the new remainder 6,and apply the division lemma to get
11 = 6 x 1 + 5
We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get
6 = 5 x 1 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 676 and 419 is 1
Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(11,6) = HCF(28,11) = HCF(67,28) = HCF(95,67) = HCF(162,95) = HCF(257,162) = HCF(419,257) = HCF(676,419) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 434 > 1, we apply the division lemma to 434 and 1, to get
434 = 1 x 434 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 434 is 1
Notice that 1 = HCF(434,1) .
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Frequently Asked Questions on HCF of 676, 419, 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 676, 419, 434?
Answer: HCF of 676, 419, 434 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 676, 419, 434 using Euclid's Algorithm?
Answer: For arbitrary numbers 676, 419, 434 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.