Highest Common Factor of 471, 1700, 5506 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 471, 1700, 5506 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 471, 1700, 5506 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 471, 1700, 5506 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 471, 1700, 5506 is 1.
HCF(471, 1700, 5506) = 1
HCF of 471, 1700, 5506 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 471, 1700, 5506 is 1.
Highest Common Factor of 471,1700,5506 is 1
Step 1: Since 1700 > 471, we apply the division lemma to 1700 and 471, to get
1700 = 471 x 3 + 287
Step 2: Since the reminder 471 ≠ 0, we apply division lemma to 287 and 471, to get
471 = 287 x 1 + 184
Step 3: We consider the new divisor 287 and the new remainder 184, and apply the division lemma to get
287 = 184 x 1 + 103
We consider the new divisor 184 and the new remainder 103,and apply the division lemma to get
184 = 103 x 1 + 81
We consider the new divisor 103 and the new remainder 81,and apply the division lemma to get
103 = 81 x 1 + 22
We consider the new divisor 81 and the new remainder 22,and apply the division lemma to get
81 = 22 x 3 + 15
We consider the new divisor 22 and the new remainder 15,and apply the division lemma to get
22 = 15 x 1 + 7
We consider the new divisor 15 and the new remainder 7,and apply the division lemma to get
15 = 7 x 2 + 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 471 and 1700 is 1
Notice that 1 = HCF(7,1) = HCF(15,7) = HCF(22,15) = HCF(81,22) = HCF(103,81) = HCF(184,103) = HCF(287,184) = HCF(471,287) = HCF(1700,471) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 5506 > 1, we apply the division lemma to 5506 and 1, to get
5506 = 1 x 5506 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 5506 is 1
Notice that 1 = HCF(5506,1) .
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Frequently Asked Questions on HCF of 471, 1700, 5506 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 471, 1700, 5506?
Answer: HCF of 471, 1700, 5506 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 471, 1700, 5506 using Euclid's Algorithm?
Answer: For arbitrary numbers 471, 1700, 5506 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
