Highest Common Factor of 557, 1458, 6934 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 557, 1458, 6934 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 557, 1458, 6934 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 557, 1458, 6934 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 557, 1458, 6934 is 1.
HCF(557, 1458, 6934) = 1
HCF of 557, 1458, 6934 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 557, 1458, 6934 is 1.
Highest Common Factor of 557,1458,6934 is 1
Step 1: Since 1458 > 557, we apply the division lemma to 1458 and 557, to get
1458 = 557 x 2 + 344
Step 2: Since the reminder 557 ≠ 0, we apply division lemma to 344 and 557, to get
557 = 344 x 1 + 213
Step 3: We consider the new divisor 344 and the new remainder 213, and apply the division lemma to get
344 = 213 x 1 + 131
We consider the new divisor 213 and the new remainder 131,and apply the division lemma to get
213 = 131 x 1 + 82
We consider the new divisor 131 and the new remainder 82,and apply the division lemma to get
131 = 82 x 1 + 49
We consider the new divisor 82 and the new remainder 49,and apply the division lemma to get
82 = 49 x 1 + 33
We consider the new divisor 49 and the new remainder 33,and apply the division lemma to get
49 = 33 x 1 + 16
We consider the new divisor 33 and the new remainder 16,and apply the division lemma to get
33 = 16 x 2 + 1
We consider the new divisor 16 and the new remainder 1,and apply the division lemma to get
16 = 1 x 16 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 557 and 1458 is 1
Notice that 1 = HCF(16,1) = HCF(33,16) = HCF(49,33) = HCF(82,49) = HCF(131,82) = HCF(213,131) = HCF(344,213) = HCF(557,344) = HCF(1458,557) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 6934 > 1, we apply the division lemma to 6934 and 1, to get
6934 = 1 x 6934 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 6934 is 1
Notice that 1 = HCF(6934,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 557, 1458, 6934 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 557, 1458, 6934?
Answer: HCF of 557, 1458, 6934 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 557, 1458, 6934 using Euclid's Algorithm?
Answer: For arbitrary numbers 557, 1458, 6934 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
