Highest Common Factor of 820, 600, 65 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 820, 600, 65 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 820, 600, 65 is 5 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 820, 600, 65 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 820, 600, 65 is 5.
HCF(820, 600, 65) = 5
HCF of 820, 600, 65 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 820, 600, 65 is 5.
Highest Common Factor of 820,600,65 is 5
Step 1: Since 820 > 600, we apply the division lemma to 820 and 600, to get
820 = 600 x 1 + 220
Step 2: Since the reminder 600 ≠ 0, we apply division lemma to 220 and 600, to get
600 = 220 x 2 + 160
Step 3: We consider the new divisor 220 and the new remainder 160, and apply the division lemma to get
220 = 160 x 1 + 60
We consider the new divisor 160 and the new remainder 60,and apply the division lemma to get
160 = 60 x 2 + 40
We consider the new divisor 60 and the new remainder 40,and apply the division lemma to get
60 = 40 x 1 + 20
We consider the new divisor 40 and the new remainder 20,and apply the division lemma to get
40 = 20 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 20, the HCF of 820 and 600 is 20
Notice that 20 = HCF(40,20) = HCF(60,40) = HCF(160,60) = HCF(220,160) = HCF(600,220) = HCF(820,600) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 65 > 20, we apply the division lemma to 65 and 20, to get
65 = 20 x 3 + 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 65 is 5
Notice that 5 = HCF(20,5) = HCF(65,20) .
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Frequently Asked Questions on HCF of 820, 600, 65 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 820, 600, 65?
Answer: HCF of 820, 600, 65 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 820, 600, 65 using Euclid's Algorithm?
Answer: For arbitrary numbers 820, 600, 65 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.