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 530, 854, 204 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 530, 854, 204 is 2 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 530, 854, 204 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 530, 854, 204 is 2.
HCF(530, 854, 204) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 530, 854, 204 is 2.
Step 1: Since 854 > 530, we apply the division lemma to 854 and 530, to get
854 = 530 x 1 + 324
Step 2: Since the reminder 530 ≠ 0, we apply division lemma to 324 and 530, to get
530 = 324 x 1 + 206
Step 3: We consider the new divisor 324 and the new remainder 206, and apply the division lemma to get
324 = 206 x 1 + 118
We consider the new divisor 206 and the new remainder 118,and apply the division lemma to get
206 = 118 x 1 + 88
We consider the new divisor 118 and the new remainder 88,and apply the division lemma to get
118 = 88 x 1 + 30
We consider the new divisor 88 and the new remainder 30,and apply the division lemma to get
88 = 30 x 2 + 28
We consider the new divisor 30 and the new remainder 28,and apply the division lemma to get
30 = 28 x 1 + 2
We consider the new divisor 28 and the new remainder 2,and apply the division lemma to get
28 = 2 x 14 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 530 and 854 is 2
Notice that 2 = HCF(28,2) = HCF(30,28) = HCF(88,30) = HCF(118,88) = HCF(206,118) = HCF(324,206) = HCF(530,324) = HCF(854,530) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 204 > 2, we apply the division lemma to 204 and 2, to get
204 = 2 x 102 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 204 is 2
Notice that 2 = HCF(204,2) .
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 530, 854, 204?
Answer: HCF of 530, 854, 204 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 530, 854, 204 using Euclid's Algorithm?
Answer: For arbitrary numbers 530, 854, 204 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.