Highest Common Factor of 612, 826, 38 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 612, 826, 38 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 612, 826, 38 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 612, 826, 38 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 612, 826, 38 is 2.
HCF(612, 826, 38) = 2
HCF of 612, 826, 38 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 612, 826, 38 is 2.
Highest Common Factor of 612,826,38 is 2
Step 1: Since 826 > 612, we apply the division lemma to 826 and 612, to get
826 = 612 x 1 + 214
Step 2: Since the reminder 612 ≠ 0, we apply division lemma to 214 and 612, to get
612 = 214 x 2 + 184
Step 3: We consider the new divisor 214 and the new remainder 184, and apply the division lemma to get
214 = 184 x 1 + 30
We consider the new divisor 184 and the new remainder 30,and apply the division lemma to get
184 = 30 x 6 + 4
We consider the new divisor 30 and the new remainder 4,and apply the division lemma to get
30 = 4 x 7 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 612 and 826 is 2
Notice that 2 = HCF(4,2) = HCF(30,4) = HCF(184,30) = HCF(214,184) = HCF(612,214) = HCF(826,612) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 38 > 2, we apply the division lemma to 38 and 2, to get
38 = 2 x 19 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 38 is 2
Notice that 2 = HCF(38,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 612, 826, 38 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 612, 826, 38?
Answer: HCF of 612, 826, 38 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 612, 826, 38 using Euclid's Algorithm?
Answer: For arbitrary numbers 612, 826, 38 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.