Highest Common Factor of 707, 405, 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 707, 405, 20 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 707, 405, 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 707, 405, 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 707, 405, 20 is 1.
HCF(707, 405, 20) = 1
HCF of 707, 405, 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 707, 405, 20 is 1.
Highest Common Factor of 707,405,20 is 1
Step 1: Since 707 > 405, we apply the division lemma to 707 and 405, to get
707 = 405 x 1 + 302
Step 2: Since the reminder 405 ≠ 0, we apply division lemma to 302 and 405, to get
405 = 302 x 1 + 103
Step 3: We consider the new divisor 302 and the new remainder 103, and apply the division lemma to get
302 = 103 x 2 + 96
We consider the new divisor 103 and the new remainder 96,and apply the division lemma to get
103 = 96 x 1 + 7
We consider the new divisor 96 and the new remainder 7,and apply the division lemma to get
96 = 7 x 13 + 5
We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get
7 = 5 x 1 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 707 and 405 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(96,7) = HCF(103,96) = HCF(302,103) = HCF(405,302) = HCF(707,405) .
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 707, 405, 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 707, 405, 20?
Answer: HCF of 707, 405, 20 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 707, 405, 20 using Euclid's Algorithm?
Answer: For arbitrary numbers 707, 405, 20 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.