Highest Common Factor of 823, 317, 749 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 823, 317, 749 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 823, 317, 749 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 823, 317, 749 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 823, 317, 749 is 1.
HCF(823, 317, 749) = 1
HCF of 823, 317, 749 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 823, 317, 749 is 1.
Highest Common Factor of 823,317,749 is 1
Step 1: Since 823 > 317, we apply the division lemma to 823 and 317, to get
823 = 317 x 2 + 189
Step 2: Since the reminder 317 ≠ 0, we apply division lemma to 189 and 317, to get
317 = 189 x 1 + 128
Step 3: We consider the new divisor 189 and the new remainder 128, and apply the division lemma to get
189 = 128 x 1 + 61
We consider the new divisor 128 and the new remainder 61,and apply the division lemma to get
128 = 61 x 2 + 6
We consider the new divisor 61 and the new remainder 6,and apply the division lemma to get
61 = 6 x 10 + 1
We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 823 and 317 is 1
Notice that 1 = HCF(6,1) = HCF(61,6) = HCF(128,61) = HCF(189,128) = HCF(317,189) = HCF(823,317) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 749 > 1, we apply the division lemma to 749 and 1, to get
749 = 1 x 749 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 749 is 1
Notice that 1 = HCF(749,1) .
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Frequently Asked Questions on HCF of 823, 317, 749 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 823, 317, 749?
Answer: HCF of 823, 317, 749 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 823, 317, 749 using Euclid's Algorithm?
Answer: For arbitrary numbers 823, 317, 749 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.