Highest Common Factor of 824, 598, 838 using Euclid's algorithm
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 824, 598, 838 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 824, 598, 838 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 824, 598, 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 824, 598, 838 is 2.
HCF(824, 598, 838) = 2
HCF of 824, 598, 838 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 824, 598, 838 is 2.
Highest Common Factor of 824,598,838 is 2
Step 1: Since 824 > 598, we apply the division lemma to 824 and 598, to get
824 = 598 x 1 + 226
Step 2: Since the reminder 598 ≠ 0, we apply division lemma to 226 and 598, to get
598 = 226 x 2 + 146
Step 3: We consider the new divisor 226 and the new remainder 146, and apply the division lemma to get
226 = 146 x 1 + 80
We consider the new divisor 146 and the new remainder 80,and apply the division lemma to get
146 = 80 x 1 + 66
We consider the new divisor 80 and the new remainder 66,and apply the division lemma to get
80 = 66 x 1 + 14
We consider the new divisor 66 and the new remainder 14,and apply the division lemma to get
66 = 14 x 4 + 10
We consider the new divisor 14 and the new remainder 10,and apply the division lemma to get
14 = 10 x 1 + 4
We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get
10 = 4 x 2 + 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 824 and 598 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(14,10) = HCF(66,14) = HCF(80,66) = HCF(146,80) = HCF(226,146) = HCF(598,226) = HCF(824,598) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 838 > 2, we apply the division lemma to 838 and 2, to get
838 = 2 x 419 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 838 is 2
Notice that 2 = HCF(838,2) .
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Frequently Asked Questions on HCF of 824, 598, 838 using Euclid's Algorithm
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 824, 598, 838?
Answer: HCF of 824, 598, 838 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 824, 598, 838 using Euclid's Algorithm?
Answer: For arbitrary numbers 824, 598, 838 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.