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 410, 709, 873 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 410, 709, 873 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 410, 709, 873 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 410, 709, 873 is 1.
HCF(410, 709, 873) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 410, 709, 873 is 1.
Step 1: Since 709 > 410, we apply the division lemma to 709 and 410, to get
709 = 410 x 1 + 299
Step 2: Since the reminder 410 ≠ 0, we apply division lemma to 299 and 410, to get
410 = 299 x 1 + 111
Step 3: We consider the new divisor 299 and the new remainder 111, and apply the division lemma to get
299 = 111 x 2 + 77
We consider the new divisor 111 and the new remainder 77,and apply the division lemma to get
111 = 77 x 1 + 34
We consider the new divisor 77 and the new remainder 34,and apply the division lemma to get
77 = 34 x 2 + 9
We consider the new divisor 34 and the new remainder 9,and apply the division lemma to get
34 = 9 x 3 + 7
We consider the new divisor 9 and the new remainder 7,and apply the division lemma to get
9 = 7 x 1 + 2
We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get
7 = 2 x 3 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 410 and 709 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(9,7) = HCF(34,9) = HCF(77,34) = HCF(111,77) = HCF(299,111) = HCF(410,299) = HCF(709,410) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 873 > 1, we apply the division lemma to 873 and 1, to get
873 = 1 x 873 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 873 is 1
Notice that 1 = HCF(873,1) .
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 410, 709, 873?
Answer: HCF of 410, 709, 873 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 410, 709, 873 using Euclid's Algorithm?
Answer: For arbitrary numbers 410, 709, 873 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.