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 246, 408, 814 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 246, 408, 814 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 246, 408, 814 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 246, 408, 814 is 2.
HCF(246, 408, 814) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 246, 408, 814 is 2.
Step 1: Since 408 > 246, we apply the division lemma to 408 and 246, to get
408 = 246 x 1 + 162
Step 2: Since the reminder 246 ≠ 0, we apply division lemma to 162 and 246, to get
246 = 162 x 1 + 84
Step 3: We consider the new divisor 162 and the new remainder 84, and apply the division lemma to get
162 = 84 x 1 + 78
We consider the new divisor 84 and the new remainder 78,and apply the division lemma to get
84 = 78 x 1 + 6
We consider the new divisor 78 and the new remainder 6,and apply the division lemma to get
78 = 6 x 13 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 246 and 408 is 6
Notice that 6 = HCF(78,6) = HCF(84,78) = HCF(162,84) = HCF(246,162) = HCF(408,246) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 814 > 6, we apply the division lemma to 814 and 6, to get
814 = 6 x 135 + 4
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 4 and 6, to get
6 = 4 x 1 + 2
Step 3: 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 6 and 814 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(814,6) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 246, 408, 814?
Answer: HCF of 246, 408, 814 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 246, 408, 814 using Euclid's Algorithm?
Answer: For arbitrary numbers 246, 408, 814 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.