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 415, 576, 814 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 415, 576, 814 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 415, 576, 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 415, 576, 814 is 1.
HCF(415, 576, 814) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 415, 576, 814 is 1.
Step 1: Since 576 > 415, we apply the division lemma to 576 and 415, to get
576 = 415 x 1 + 161
Step 2: Since the reminder 415 ≠ 0, we apply division lemma to 161 and 415, to get
415 = 161 x 2 + 93
Step 3: We consider the new divisor 161 and the new remainder 93, and apply the division lemma to get
161 = 93 x 1 + 68
We consider the new divisor 93 and the new remainder 68,and apply the division lemma to get
93 = 68 x 1 + 25
We consider the new divisor 68 and the new remainder 25,and apply the division lemma to get
68 = 25 x 2 + 18
We consider the new divisor 25 and the new remainder 18,and apply the division lemma to get
25 = 18 x 1 + 7
We consider the new divisor 18 and the new remainder 7,and apply the division lemma to get
18 = 7 x 2 + 4
We consider the new divisor 7 and the new remainder 4,and apply the division lemma to get
7 = 4 x 1 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 415 and 576 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(18,7) = HCF(25,18) = HCF(68,25) = HCF(93,68) = HCF(161,93) = HCF(415,161) = HCF(576,415) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 814 > 1, we apply the division lemma to 814 and 1, to get
814 = 1 x 814 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 814 is 1
Notice that 1 = HCF(814,1) .
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 415, 576, 814?
Answer: HCF of 415, 576, 814 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 415, 576, 814 using Euclid's Algorithm?
Answer: For arbitrary numbers 415, 576, 814 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.