Highest Common Factor of 431, 578, 81, 724 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, 578, 81, 724 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 431, 578, 81, 724 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, 578, 81, 724 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, 578, 81, 724 is 1.
HCF(431, 578, 81, 724) = 1
HCF of 431, 578, 81, 724 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, 578, 81, 724 is 1.
Highest Common Factor of 431,578,81,724 is 1
Step 1: Since 578 > 431, we apply the division lemma to 578 and 431, to get
578 = 431 x 1 + 147
Step 2: Since the reminder 431 ≠ 0, we apply division lemma to 147 and 431, to get
431 = 147 x 2 + 137
Step 3: We consider the new divisor 147 and the new remainder 137, and apply the division lemma to get
147 = 137 x 1 + 10
We consider the new divisor 137 and the new remainder 10,and apply the division lemma to get
137 = 10 x 13 + 7
We consider the new divisor 10 and the new remainder 7,and apply the division lemma to get
10 = 7 x 1 + 3
We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get
7 = 3 x 2 + 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 431 and 578 is 1
Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(10,7) = HCF(137,10) = HCF(147,137) = HCF(431,147) = HCF(578,431) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 81 > 1, we apply the division lemma to 81 and 1, to get
81 = 1 x 81 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 81 is 1
Notice that 1 = HCF(81,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 724 > 1, we apply the division lemma to 724 and 1, to get
724 = 1 x 724 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 724 is 1
Notice that 1 = HCF(724,1) .
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Frequently Asked Questions on HCF of 431, 578, 81, 724 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, 578, 81, 724?
Answer: HCF of 431, 578, 81, 724 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 431, 578, 81, 724 using Euclid's Algorithm?
Answer: For arbitrary numbers 431, 578, 81, 724 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.