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 582, 909, 203 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 582, 909, 203 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 582, 909, 203 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 582, 909, 203 is 1.
HCF(582, 909, 203) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 582, 909, 203 is 1.
Step 1: Since 909 > 582, we apply the division lemma to 909 and 582, to get
909 = 582 x 1 + 327
Step 2: Since the reminder 582 ≠ 0, we apply division lemma to 327 and 582, to get
582 = 327 x 1 + 255
Step 3: We consider the new divisor 327 and the new remainder 255, and apply the division lemma to get
327 = 255 x 1 + 72
We consider the new divisor 255 and the new remainder 72,and apply the division lemma to get
255 = 72 x 3 + 39
We consider the new divisor 72 and the new remainder 39,and apply the division lemma to get
72 = 39 x 1 + 33
We consider the new divisor 39 and the new remainder 33,and apply the division lemma to get
39 = 33 x 1 + 6
We consider the new divisor 33 and the new remainder 6,and apply the division lemma to get
33 = 6 x 5 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 582 and 909 is 3
Notice that 3 = HCF(6,3) = HCF(33,6) = HCF(39,33) = HCF(72,39) = HCF(255,72) = HCF(327,255) = HCF(582,327) = HCF(909,582) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 203 > 3, we apply the division lemma to 203 and 3, to get
203 = 3 x 67 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: 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 3 and 203 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(203,3) .
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 582, 909, 203?
Answer: HCF of 582, 909, 203 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 582, 909, 203 using Euclid's Algorithm?
Answer: For arbitrary numbers 582, 909, 203 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.