Highest Common Factor of 20, 85, 705, 417 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 20, 85, 705, 417 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 20, 85, 705, 417 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 20, 85, 705, 417 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 20, 85, 705, 417 is 1.
HCF(20, 85, 705, 417) = 1
HCF of 20, 85, 705, 417 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 20, 85, 705, 417 is 1.
Highest Common Factor of 20,85,705,417 is 1
Step 1: Since 85 > 20, we apply the division lemma to 85 and 20, to get
85 = 20 x 4 + 5
Step 2: Since the reminder 20 ≠ 0, we apply division lemma to 5 and 20, to get
20 = 5 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 20 and 85 is 5
Notice that 5 = HCF(20,5) = HCF(85,20) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 705 > 5, we apply the division lemma to 705 and 5, to get
705 = 5 x 141 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 5 and 705 is 5
Notice that 5 = HCF(705,5) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 417 > 5, we apply the division lemma to 417 and 5, to get
417 = 5 x 83 + 2
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 2 and 5, to get
5 = 2 x 2 + 1
Step 3: 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 5 and 417 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(417,5) .
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Frequently Asked Questions on HCF of 20, 85, 705, 417 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 20, 85, 705, 417?
Answer: HCF of 20, 85, 705, 417 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 20, 85, 705, 417 using Euclid's Algorithm?
Answer: For arbitrary numbers 20, 85, 705, 417 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.