Highest Common Factor of 310, 431 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 310, 431 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 310, 431 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 310, 431 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 310, 431 is 1.
HCF(310, 431) = 1
HCF of 310, 431 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 310, 431 is 1.
Highest Common Factor of 310,431 is 1
Step 1: Since 431 > 310, we apply the division lemma to 431 and 310, to get
431 = 310 x 1 + 121
Step 2: Since the reminder 310 ≠ 0, we apply division lemma to 121 and 310, to get
310 = 121 x 2 + 68
Step 3: We consider the new divisor 121 and the new remainder 68, and apply the division lemma to get
121 = 68 x 1 + 53
We consider the new divisor 68 and the new remainder 53,and apply the division lemma to get
68 = 53 x 1 + 15
We consider the new divisor 53 and the new remainder 15,and apply the division lemma to get
53 = 15 x 3 + 8
We consider the new divisor 15 and the new remainder 8,and apply the division lemma to get
15 = 8 x 1 + 7
We consider the new divisor 8 and the new remainder 7,and apply the division lemma to get
8 = 7 x 1 + 1
We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 310 and 431 is 1
Notice that 1 = HCF(7,1) = HCF(8,7) = HCF(15,8) = HCF(53,15) = HCF(68,53) = HCF(121,68) = HCF(310,121) = HCF(431,310) .
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Frequently Asked Questions on HCF of 310, 431 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 310, 431?
Answer: HCF of 310, 431 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 310, 431 using Euclid's Algorithm?
Answer: For arbitrary numbers 310, 431 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.