Highest Common Factor of 431, 343, 72 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 431, 343, 72 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 431, 343, 72 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 431, 343, 72 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 431, 343, 72 is 1.
HCF(431, 343, 72) = 1
HCF of 431, 343, 72 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 431, 343, 72 is 1.
Highest Common Factor of 431,343,72 is 1
Step 1: Since 431 > 343, we apply the division lemma to 431 and 343, to get
431 = 343 x 1 + 88
Step 2: Since the reminder 343 ≠ 0, we apply division lemma to 88 and 343, to get
343 = 88 x 3 + 79
Step 3: We consider the new divisor 88 and the new remainder 79, and apply the division lemma to get
88 = 79 x 1 + 9
We consider the new divisor 79 and the new remainder 9,and apply the division lemma to get
79 = 9 x 8 + 7
We consider the new divisor 9 and the new remainder 7,and apply the division lemma to get
9 = 7 x 1 + 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 431 and 343 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(9,7) = HCF(79,9) = HCF(88,79) = HCF(343,88) = HCF(431,343) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 72 > 1, we apply the division lemma to 72 and 1, to get
72 = 1 x 72 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 72 is 1
Notice that 1 = HCF(72,1) .
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Frequently Asked Questions on HCF of 431, 343, 72 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 431, 343, 72?
Answer: HCF of 431, 343, 72 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 431, 343, 72 using Euclid's Algorithm?
Answer: For arbitrary numbers 431, 343, 72 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.