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 857, 6743, 4539 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 857, 6743, 4539 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 857, 6743, 4539 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 857, 6743, 4539 is 1.
HCF(857, 6743, 4539) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 857, 6743, 4539 is 1.
Step 1: Since 6743 > 857, we apply the division lemma to 6743 and 857, to get
6743 = 857 x 7 + 744
Step 2: Since the reminder 857 ≠ 0, we apply division lemma to 744 and 857, to get
857 = 744 x 1 + 113
Step 3: We consider the new divisor 744 and the new remainder 113, and apply the division lemma to get
744 = 113 x 6 + 66
We consider the new divisor 113 and the new remainder 66,and apply the division lemma to get
113 = 66 x 1 + 47
We consider the new divisor 66 and the new remainder 47,and apply the division lemma to get
66 = 47 x 1 + 19
We consider the new divisor 47 and the new remainder 19,and apply the division lemma to get
47 = 19 x 2 + 9
We consider the new divisor 19 and the new remainder 9,and apply the division lemma to get
19 = 9 x 2 + 1
We consider the new divisor 9 and the new remainder 1,and apply the division lemma to get
9 = 1 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 857 and 6743 is 1
Notice that 1 = HCF(9,1) = HCF(19,9) = HCF(47,19) = HCF(66,47) = HCF(113,66) = HCF(744,113) = HCF(857,744) = HCF(6743,857) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 4539 > 1, we apply the division lemma to 4539 and 1, to get
4539 = 1 x 4539 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 4539 is 1
Notice that 1 = HCF(4539,1) .
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 857, 6743, 4539?
Answer: HCF of 857, 6743, 4539 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 857, 6743, 4539 using Euclid's Algorithm?
Answer: For arbitrary numbers 857, 6743, 4539 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.