Highest Common Factor of 709, 578, 126 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 709, 578, 126 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 709, 578, 126 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 709, 578, 126 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 709, 578, 126 is 1.
HCF(709, 578, 126) = 1
HCF of 709, 578, 126 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 709, 578, 126 is 1.
Highest Common Factor of 709,578,126 is 1
Step 1: Since 709 > 578, we apply the division lemma to 709 and 578, to get
709 = 578 x 1 + 131
Step 2: Since the reminder 578 ≠ 0, we apply division lemma to 131 and 578, to get
578 = 131 x 4 + 54
Step 3: We consider the new divisor 131 and the new remainder 54, and apply the division lemma to get
131 = 54 x 2 + 23
We consider the new divisor 54 and the new remainder 23,and apply the division lemma to get
54 = 23 x 2 + 8
We consider the new divisor 23 and the new remainder 8,and apply the division lemma to get
23 = 8 x 2 + 7
We consider the new divisor 8 and the new remainder 7,and apply the division lemma to get
8 = 7 x 1 + 1
We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 709 and 578 is 1
Notice that 1 = HCF(7,1) = HCF(8,7) = HCF(23,8) = HCF(54,23) = HCF(131,54) = HCF(578,131) = HCF(709,578) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 126 > 1, we apply the division lemma to 126 and 1, to get
126 = 1 x 126 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 126 is 1
Notice that 1 = HCF(126,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 709, 578, 126 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 709, 578, 126?
Answer: HCF of 709, 578, 126 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 709, 578, 126 using Euclid's Algorithm?
Answer: For arbitrary numbers 709, 578, 126 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.