Highest Common Factor of 160, 205, 828 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 160, 205, 828 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 160, 205, 828 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 160, 205, 828 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 160, 205, 828 is 1.
HCF(160, 205, 828) = 1
HCF of 160, 205, 828 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 160, 205, 828 is 1.
Highest Common Factor of 160,205,828 is 1
Step 1: Since 205 > 160, we apply the division lemma to 205 and 160, to get
205 = 160 x 1 + 45
Step 2: Since the reminder 160 ≠ 0, we apply division lemma to 45 and 160, to get
160 = 45 x 3 + 25
Step 3: We consider the new divisor 45 and the new remainder 25, and apply the division lemma to get
45 = 25 x 1 + 20
We consider the new divisor 25 and the new remainder 20,and apply the division lemma to get
25 = 20 x 1 + 5
We consider the new divisor 20 and the new remainder 5,and apply the division lemma 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 160 and 205 is 5
Notice that 5 = HCF(20,5) = HCF(25,20) = HCF(45,25) = HCF(160,45) = HCF(205,160) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 828 > 5, we apply the division lemma to 828 and 5, to get
828 = 5 x 165 + 3
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 3 and 5, to get
5 = 3 x 1 + 2
Step 3: We consider the new divisor 3 and the new remainder 2, and apply the division lemma to get
3 = 2 x 1 + 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 5 and 828 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(828,5) .
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Frequently Asked Questions on HCF of 160, 205, 828 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 160, 205, 828?
Answer: HCF of 160, 205, 828 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 160, 205, 828 using Euclid's Algorithm?
Answer: For arbitrary numbers 160, 205, 828 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.