Highest Common Factor of 3718, 8306, 18157 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 3718, 8306, 18157 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 3718, 8306, 18157 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 3718, 8306, 18157 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 3718, 8306, 18157 is 1.
HCF(3718, 8306, 18157) = 1
HCF of 3718, 8306, 18157 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 3718, 8306, 18157 is 1.
Highest Common Factor of 3718,8306,18157 is 1
Step 1: Since 8306 > 3718, we apply the division lemma to 8306 and 3718, to get
8306 = 3718 x 2 + 870
Step 2: Since the reminder 3718 ≠ 0, we apply division lemma to 870 and 3718, to get
3718 = 870 x 4 + 238
Step 3: We consider the new divisor 870 and the new remainder 238, and apply the division lemma to get
870 = 238 x 3 + 156
We consider the new divisor 238 and the new remainder 156,and apply the division lemma to get
238 = 156 x 1 + 82
We consider the new divisor 156 and the new remainder 82,and apply the division lemma to get
156 = 82 x 1 + 74
We consider the new divisor 82 and the new remainder 74,and apply the division lemma to get
82 = 74 x 1 + 8
We consider the new divisor 74 and the new remainder 8,and apply the division lemma to get
74 = 8 x 9 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 3718 and 8306 is 2
Notice that 2 = HCF(8,2) = HCF(74,8) = HCF(82,74) = HCF(156,82) = HCF(238,156) = HCF(870,238) = HCF(3718,870) = HCF(8306,3718) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 18157 > 2, we apply the division lemma to 18157 and 2, to get
18157 = 2 x 9078 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 18157 is 1
Notice that 1 = HCF(2,1) = HCF(18157,2) .
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Frequently Asked Questions on HCF of 3718, 8306, 18157 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 3718, 8306, 18157?
Answer: HCF of 3718, 8306, 18157 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 3718, 8306, 18157 using Euclid's Algorithm?
Answer: For arbitrary numbers 3718, 8306, 18157 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.