Highest Common Factor of 310, 513, 622 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, 513, 622 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 310, 513, 622 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, 513, 622 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, 513, 622 is 1.
HCF(310, 513, 622) = 1
HCF of 310, 513, 622 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, 513, 622 is 1.
Highest Common Factor of 310,513,622 is 1
Step 1: Since 513 > 310, we apply the division lemma to 513 and 310, to get
513 = 310 x 1 + 203
Step 2: Since the reminder 310 ≠ 0, we apply division lemma to 203 and 310, to get
310 = 203 x 1 + 107
Step 3: We consider the new divisor 203 and the new remainder 107, and apply the division lemma to get
203 = 107 x 1 + 96
We consider the new divisor 107 and the new remainder 96,and apply the division lemma to get
107 = 96 x 1 + 11
We consider the new divisor 96 and the new remainder 11,and apply the division lemma to get
96 = 11 x 8 + 8
We consider the new divisor 11 and the new remainder 8,and apply the division lemma to get
11 = 8 x 1 + 3
We consider the new divisor 8 and the new remainder 3,and apply the division lemma to get
8 = 3 x 2 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 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 310 and 513 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(11,8) = HCF(96,11) = HCF(107,96) = HCF(203,107) = HCF(310,203) = HCF(513,310) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 622 > 1, we apply the division lemma to 622 and 1, to get
622 = 1 x 622 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 622 is 1
Notice that 1 = HCF(622,1) .
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Frequently Asked Questions on HCF of 310, 513, 622 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, 513, 622?
Answer: HCF of 310, 513, 622 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 310, 513, 622 using Euclid's Algorithm?
Answer: For arbitrary numbers 310, 513, 622 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.