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 914, 582, 589 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 914, 582, 589 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 914, 582, 589 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 914, 582, 589 is 1.
HCF(914, 582, 589) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 914, 582, 589 is 1.
Step 1: Since 914 > 582, we apply the division lemma to 914 and 582, to get
914 = 582 x 1 + 332
Step 2: Since the reminder 582 ≠ 0, we apply division lemma to 332 and 582, to get
582 = 332 x 1 + 250
Step 3: We consider the new divisor 332 and the new remainder 250, and apply the division lemma to get
332 = 250 x 1 + 82
We consider the new divisor 250 and the new remainder 82,and apply the division lemma to get
250 = 82 x 3 + 4
We consider the new divisor 82 and the new remainder 4,and apply the division lemma to get
82 = 4 x 20 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 914 and 582 is 2
Notice that 2 = HCF(4,2) = HCF(82,4) = HCF(250,82) = HCF(332,250) = HCF(582,332) = HCF(914,582) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 589 > 2, we apply the division lemma to 589 and 2, to get
589 = 2 x 294 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 589 is 1
Notice that 1 = HCF(2,1) = HCF(589,2) .
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 914, 582, 589?
Answer: HCF of 914, 582, 589 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 914, 582, 589 using Euclid's Algorithm?
Answer: For arbitrary numbers 914, 582, 589 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.