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 643, 509, 865 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 643, 509, 865 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 643, 509, 865 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 643, 509, 865 is 1.
HCF(643, 509, 865) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 643, 509, 865 is 1.
Step 1: Since 643 > 509, we apply the division lemma to 643 and 509, to get
643 = 509 x 1 + 134
Step 2: Since the reminder 509 ≠ 0, we apply division lemma to 134 and 509, to get
509 = 134 x 3 + 107
Step 3: We consider the new divisor 134 and the new remainder 107, and apply the division lemma to get
134 = 107 x 1 + 27
We consider the new divisor 107 and the new remainder 27,and apply the division lemma to get
107 = 27 x 3 + 26
We consider the new divisor 27 and the new remainder 26,and apply the division lemma to get
27 = 26 x 1 + 1
We consider the new divisor 26 and the new remainder 1,and apply the division lemma to get
26 = 1 x 26 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 643 and 509 is 1
Notice that 1 = HCF(26,1) = HCF(27,26) = HCF(107,27) = HCF(134,107) = HCF(509,134) = HCF(643,509) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 865 > 1, we apply the division lemma to 865 and 1, to get
865 = 1 x 865 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 865 is 1
Notice that 1 = HCF(865,1) .
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 643, 509, 865?
Answer: HCF of 643, 509, 865 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 643, 509, 865 using Euclid's Algorithm?
Answer: For arbitrary numbers 643, 509, 865 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.