Highest Common Factor of 477, 823, 170 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 477, 823, 170 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 477, 823, 170 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 477, 823, 170 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 477, 823, 170 is 1.
HCF(477, 823, 170) = 1
HCF of 477, 823, 170 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 477, 823, 170 is 1.
Highest Common Factor of 477,823,170 is 1
Step 1: Since 823 > 477, we apply the division lemma to 823 and 477, to get
823 = 477 x 1 + 346
Step 2: Since the reminder 477 ≠ 0, we apply division lemma to 346 and 477, to get
477 = 346 x 1 + 131
Step 3: We consider the new divisor 346 and the new remainder 131, and apply the division lemma to get
346 = 131 x 2 + 84
We consider the new divisor 131 and the new remainder 84,and apply the division lemma to get
131 = 84 x 1 + 47
We consider the new divisor 84 and the new remainder 47,and apply the division lemma to get
84 = 47 x 1 + 37
We consider the new divisor 47 and the new remainder 37,and apply the division lemma to get
47 = 37 x 1 + 10
We consider the new divisor 37 and the new remainder 10,and apply the division lemma to get
37 = 10 x 3 + 7
We consider the new divisor 10 and the new remainder 7,and apply the division lemma to get
10 = 7 x 1 + 3
We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get
7 = 3 x 2 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 477 and 823 is 1
Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(10,7) = HCF(37,10) = HCF(47,37) = HCF(84,47) = HCF(131,84) = HCF(346,131) = HCF(477,346) = HCF(823,477) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 170 > 1, we apply the division lemma to 170 and 1, to get
170 = 1 x 170 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 170 is 1
Notice that 1 = HCF(170,1) .
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Frequently Asked Questions on HCF of 477, 823, 170 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 477, 823, 170?
Answer: HCF of 477, 823, 170 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 477, 823, 170 using Euclid's Algorithm?
Answer: For arbitrary numbers 477, 823, 170 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.