Highest Common Factor of 220, 820, 138 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 220, 820, 138 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 220, 820, 138 is 2 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 220, 820, 138 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 220, 820, 138 is 2.
HCF(220, 820, 138) = 2
HCF of 220, 820, 138 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 220, 820, 138 is 2.
Highest Common Factor of 220,820,138 is 2
Step 1: Since 820 > 220, we apply the division lemma to 820 and 220, to get
820 = 220 x 3 + 160
Step 2: Since the reminder 220 ≠ 0, we apply division lemma to 160 and 220, to get
220 = 160 x 1 + 60
Step 3: 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 220 and 820 is 20
Notice that 20 = HCF(40,20) = HCF(60,40) = HCF(160,60) = HCF(220,160) = HCF(820,220) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 138 > 20, we apply the division lemma to 138 and 20, to get
138 = 20 x 6 + 18
Step 2: Since the reminder 20 ≠ 0, we apply division lemma to 18 and 20, to get
20 = 18 x 1 + 2
Step 3: We consider the new divisor 18 and the new remainder 2, and apply the division lemma to get
18 = 2 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 20 and 138 is 2
Notice that 2 = HCF(18,2) = HCF(20,18) = HCF(138,20) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 220, 820, 138 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 220, 820, 138?
Answer: HCF of 220, 820, 138 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 220, 820, 138 using Euclid's Algorithm?
Answer: For arbitrary numbers 220, 820, 138 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.