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 583, 824, 838 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 583, 824, 838 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 583, 824, 838 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 583, 824, 838 is 1.
HCF(583, 824, 838) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 583, 824, 838 is 1.
Step 1: Since 824 > 583, we apply the division lemma to 824 and 583, to get
824 = 583 x 1 + 241
Step 2: Since the reminder 583 ≠ 0, we apply division lemma to 241 and 583, to get
583 = 241 x 2 + 101
Step 3: We consider the new divisor 241 and the new remainder 101, and apply the division lemma to get
241 = 101 x 2 + 39
We consider the new divisor 101 and the new remainder 39,and apply the division lemma to get
101 = 39 x 2 + 23
We consider the new divisor 39 and the new remainder 23,and apply the division lemma to get
39 = 23 x 1 + 16
We consider the new divisor 23 and the new remainder 16,and apply the division lemma to get
23 = 16 x 1 + 7
We consider the new divisor 16 and the new remainder 7,and apply the division lemma to get
16 = 7 x 2 + 2
We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get
7 = 2 x 3 + 1
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 583 and 824 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(16,7) = HCF(23,16) = HCF(39,23) = HCF(101,39) = HCF(241,101) = HCF(583,241) = HCF(824,583) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 838 > 1, we apply the division lemma to 838 and 1, to get
838 = 1 x 838 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 838 is 1
Notice that 1 = HCF(838,1) .
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 583, 824, 838?
Answer: HCF of 583, 824, 838 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 583, 824, 838 using Euclid's Algorithm?
Answer: For arbitrary numbers 583, 824, 838 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.