Highest Common Factor of 398, 523, 309 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 398, 523, 309 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 398, 523, 309 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 398, 523, 309 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 398, 523, 309 is 1.
HCF(398, 523, 309) = 1
HCF of 398, 523, 309 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 398, 523, 309 is 1.
Highest Common Factor of 398,523,309 is 1
Step 1: Since 523 > 398, we apply the division lemma to 523 and 398, to get
523 = 398 x 1 + 125
Step 2: Since the reminder 398 ≠ 0, we apply division lemma to 125 and 398, to get
398 = 125 x 3 + 23
Step 3: We consider the new divisor 125 and the new remainder 23, and apply the division lemma to get
125 = 23 x 5 + 10
We consider the new divisor 23 and the new remainder 10,and apply the division lemma to get
23 = 10 x 2 + 3
We consider the new divisor 10 and the new remainder 3,and apply the division lemma to get
10 = 3 x 3 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 398 and 523 is 1
Notice that 1 = HCF(3,1) = HCF(10,3) = HCF(23,10) = HCF(125,23) = HCF(398,125) = HCF(523,398) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 309 > 1, we apply the division lemma to 309 and 1, to get
309 = 1 x 309 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 309 is 1
Notice that 1 = HCF(309,1) .
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Frequently Asked Questions on HCF of 398, 523, 309 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 398, 523, 309?
Answer: HCF of 398, 523, 309 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 398, 523, 309 using Euclid's Algorithm?
Answer: For arbitrary numbers 398, 523, 309 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.