Highest Common Factor of 820, 195, 76 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, 195, 76 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 820, 195, 76 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 820, 195, 76 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, 195, 76 is 1.
HCF(820, 195, 76) = 1
HCF of 820, 195, 76 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, 195, 76 is 1.
Highest Common Factor of 820,195,76 is 1
Step 1: Since 820 > 195, we apply the division lemma to 820 and 195, to get
820 = 195 x 4 + 40
Step 2: Since the reminder 195 ≠ 0, we apply division lemma to 40 and 195, to get
195 = 40 x 4 + 35
Step 3: We consider the new divisor 40 and the new remainder 35, and apply the division lemma to get
40 = 35 x 1 + 5
We consider the new divisor 35 and the new remainder 5, and apply the division lemma to get
35 = 5 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 820 and 195 is 5
Notice that 5 = HCF(35,5) = HCF(40,35) = HCF(195,40) = HCF(820,195) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 76 > 5, we apply the division lemma to 76 and 5, to get
76 = 5 x 15 + 1
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 1 and 5, to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5 and 76 is 1
Notice that 1 = HCF(5,1) = HCF(76,5) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 820, 195, 76 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, 195, 76?
Answer: HCF of 820, 195, 76 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 820, 195, 76 using Euclid's Algorithm?
Answer: For arbitrary numbers 820, 195, 76 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.