Highest Common Factor of 709, 538, 442, 20 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, 538, 442, 20 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 709, 538, 442, 20 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, 538, 442, 20 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, 538, 442, 20 is 1.
HCF(709, 538, 442, 20) = 1
HCF of 709, 538, 442, 20 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, 538, 442, 20 is 1.
Highest Common Factor of 709,538,442,20 is 1
Step 1: Since 709 > 538, we apply the division lemma to 709 and 538, to get
709 = 538 x 1 + 171
Step 2: Since the reminder 538 ≠ 0, we apply division lemma to 171 and 538, to get
538 = 171 x 3 + 25
Step 3: We consider the new divisor 171 and the new remainder 25, and apply the division lemma to get
171 = 25 x 6 + 21
We consider the new divisor 25 and the new remainder 21,and apply the division lemma to get
25 = 21 x 1 + 4
We consider the new divisor 21 and the new remainder 4,and apply the division lemma to get
21 = 4 x 5 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 709 and 538 is 1
Notice that 1 = HCF(4,1) = HCF(21,4) = HCF(25,21) = HCF(171,25) = HCF(538,171) = HCF(709,538) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 442 > 1, we apply the division lemma to 442 and 1, to get
442 = 1 x 442 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 442 is 1
Notice that 1 = HCF(442,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 20 > 1, we apply the division lemma to 20 and 1, to get
20 = 1 x 20 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 20 is 1
Notice that 1 = HCF(20,1) .
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Frequently Asked Questions on HCF of 709, 538, 442, 20 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, 538, 442, 20?
Answer: HCF of 709, 538, 442, 20 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 709, 538, 442, 20 using Euclid's Algorithm?
Answer: For arbitrary numbers 709, 538, 442, 20 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.