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 684, 7864, 5823 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 684, 7864, 5823 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 684, 7864, 5823 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 684, 7864, 5823 is 1.
HCF(684, 7864, 5823) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 684, 7864, 5823 is 1.
Step 1: Since 7864 > 684, we apply the division lemma to 7864 and 684, to get
7864 = 684 x 11 + 340
Step 2: Since the reminder 684 ≠ 0, we apply division lemma to 340 and 684, to get
684 = 340 x 2 + 4
Step 3: We consider the new divisor 340 and the new remainder 4, and apply the division lemma to get
340 = 4 x 85 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 684 and 7864 is 4
Notice that 4 = HCF(340,4) = HCF(684,340) = HCF(7864,684) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 5823 > 4, we apply the division lemma to 5823 and 4, to get
5823 = 4 x 1455 + 3
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 3 and 4, to get
4 = 3 x 1 + 1
Step 3: 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 4 and 5823 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(5823,4) .
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 684, 7864, 5823?
Answer: HCF of 684, 7864, 5823 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 684, 7864, 5823 using Euclid's Algorithm?
Answer: For arbitrary numbers 684, 7864, 5823 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.