Highest Common Factor of 3105, 7073, 67996 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 3105, 7073, 67996 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 3105, 7073, 67996 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 3105, 7073, 67996 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 3105, 7073, 67996 is 1.
HCF(3105, 7073, 67996) = 1
HCF of 3105, 7073, 67996 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 3105, 7073, 67996 is 1.
Highest Common Factor of 3105,7073,67996 is 1
Step 1: Since 7073 > 3105, we apply the division lemma to 7073 and 3105, to get
7073 = 3105 x 2 + 863
Step 2: Since the reminder 3105 ≠ 0, we apply division lemma to 863 and 3105, to get
3105 = 863 x 3 + 516
Step 3: We consider the new divisor 863 and the new remainder 516, and apply the division lemma to get
863 = 516 x 1 + 347
We consider the new divisor 516 and the new remainder 347,and apply the division lemma to get
516 = 347 x 1 + 169
We consider the new divisor 347 and the new remainder 169,and apply the division lemma to get
347 = 169 x 2 + 9
We consider the new divisor 169 and the new remainder 9,and apply the division lemma to get
169 = 9 x 18 + 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 3105 and 7073 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(9,7) = HCF(169,9) = HCF(347,169) = HCF(516,347) = HCF(863,516) = HCF(3105,863) = HCF(7073,3105) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 67996 > 1, we apply the division lemma to 67996 and 1, to get
67996 = 1 x 67996 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 67996 is 1
Notice that 1 = HCF(67996,1) .
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Frequently Asked Questions on HCF of 3105, 7073, 67996 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 3105, 7073, 67996?
Answer: HCF of 3105, 7073, 67996 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 3105, 7073, 67996 using Euclid's Algorithm?
Answer: For arbitrary numbers 3105, 7073, 67996 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
