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 588, 819, 421 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 588, 819, 421 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 588, 819, 421 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 588, 819, 421 is 1.
HCF(588, 819, 421) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 588, 819, 421 is 1.
Step 1: Since 819 > 588, we apply the division lemma to 819 and 588, to get
819 = 588 x 1 + 231
Step 2: Since the reminder 588 ≠ 0, we apply division lemma to 231 and 588, to get
588 = 231 x 2 + 126
Step 3: We consider the new divisor 231 and the new remainder 126, and apply the division lemma to get
231 = 126 x 1 + 105
We consider the new divisor 126 and the new remainder 105,and apply the division lemma to get
126 = 105 x 1 + 21
We consider the new divisor 105 and the new remainder 21,and apply the division lemma to get
105 = 21 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 21, the HCF of 588 and 819 is 21
Notice that 21 = HCF(105,21) = HCF(126,105) = HCF(231,126) = HCF(588,231) = HCF(819,588) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 421 > 21, we apply the division lemma to 421 and 21, to get
421 = 21 x 20 + 1
Step 2: Since the reminder 21 ≠ 0, we apply division lemma to 1 and 21, to get
21 = 1 x 21 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 21 and 421 is 1
Notice that 1 = HCF(21,1) = HCF(421,21) .
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 588, 819, 421?
Answer: HCF of 588, 819, 421 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 588, 819, 421 using Euclid's Algorithm?
Answer: For arbitrary numbers 588, 819, 421 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.