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 134, 218, 809 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 134, 218, 809 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 134, 218, 809 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 134, 218, 809 is 1.
HCF(134, 218, 809) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 134, 218, 809 is 1.
Step 1: Since 218 > 134, we apply the division lemma to 218 and 134, to get
218 = 134 x 1 + 84
Step 2: Since the reminder 134 ≠ 0, we apply division lemma to 84 and 134, to get
134 = 84 x 1 + 50
Step 3: We consider the new divisor 84 and the new remainder 50, and apply the division lemma to get
84 = 50 x 1 + 34
We consider the new divisor 50 and the new remainder 34,and apply the division lemma to get
50 = 34 x 1 + 16
We consider the new divisor 34 and the new remainder 16,and apply the division lemma to get
34 = 16 x 2 + 2
We consider the new divisor 16 and the new remainder 2,and apply the division lemma to get
16 = 2 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 134 and 218 is 2
Notice that 2 = HCF(16,2) = HCF(34,16) = HCF(50,34) = HCF(84,50) = HCF(134,84) = HCF(218,134) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 809 > 2, we apply the division lemma to 809 and 2, to get
809 = 2 x 404 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 809 is 1
Notice that 1 = HCF(2,1) = HCF(809,2) .
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 134, 218, 809?
Answer: HCF of 134, 218, 809 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 134, 218, 809 using Euclid's Algorithm?
Answer: For arbitrary numbers 134, 218, 809 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.