Highest Common Factor of 3178, 1703, 51313 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 3178, 1703, 51313 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 3178, 1703, 51313 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 3178, 1703, 51313 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 3178, 1703, 51313 is 1.
HCF(3178, 1703, 51313) = 1
HCF of 3178, 1703, 51313 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 3178, 1703, 51313 is 1.
Highest Common Factor of 3178,1703,51313 is 1
Step 1: Since 3178 > 1703, we apply the division lemma to 3178 and 1703, to get
3178 = 1703 x 1 + 1475
Step 2: Since the reminder 1703 ≠ 0, we apply division lemma to 1475 and 1703, to get
1703 = 1475 x 1 + 228
Step 3: We consider the new divisor 1475 and the new remainder 228, and apply the division lemma to get
1475 = 228 x 6 + 107
We consider the new divisor 228 and the new remainder 107,and apply the division lemma to get
228 = 107 x 2 + 14
We consider the new divisor 107 and the new remainder 14,and apply the division lemma to get
107 = 14 x 7 + 9
We consider the new divisor 14 and the new remainder 9,and apply the division lemma to get
14 = 9 x 1 + 5
We consider the new divisor 9 and the new remainder 5,and apply the division lemma to get
9 = 5 x 1 + 4
We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get
5 = 4 x 1 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3178 and 1703 is 1
Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(14,9) = HCF(107,14) = HCF(228,107) = HCF(1475,228) = HCF(1703,1475) = HCF(3178,1703) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 51313 > 1, we apply the division lemma to 51313 and 1, to get
51313 = 1 x 51313 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 51313 is 1
Notice that 1 = HCF(51313,1) .
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Frequently Asked Questions on HCF of 3178, 1703, 51313 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 3178, 1703, 51313?
Answer: HCF of 3178, 1703, 51313 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 3178, 1703, 51313 using Euclid's Algorithm?
Answer: For arbitrary numbers 3178, 1703, 51313 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
