Highest Common Factor of 158, 9756, 5105 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 158, 9756, 5105 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 158, 9756, 5105 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 158, 9756, 5105 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 158, 9756, 5105 is 1.
HCF(158, 9756, 5105) = 1
HCF of 158, 9756, 5105 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 158, 9756, 5105 is 1.
Highest Common Factor of 158,9756,5105 is 1
Step 1: Since 9756 > 158, we apply the division lemma to 9756 and 158, to get
9756 = 158 x 61 + 118
Step 2: Since the reminder 158 ≠ 0, we apply division lemma to 118 and 158, to get
158 = 118 x 1 + 40
Step 3: We consider the new divisor 118 and the new remainder 40, and apply the division lemma to get
118 = 40 x 2 + 38
We consider the new divisor 40 and the new remainder 38,and apply the division lemma to get
40 = 38 x 1 + 2
We consider the new divisor 38 and the new remainder 2,and apply the division lemma to get
38 = 2 x 19 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 158 and 9756 is 2
Notice that 2 = HCF(38,2) = HCF(40,38) = HCF(118,40) = HCF(158,118) = HCF(9756,158) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 5105 > 2, we apply the division lemma to 5105 and 2, to get
5105 = 2 x 2552 + 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 5105 is 1
Notice that 1 = HCF(2,1) = HCF(5105,2) .
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Frequently Asked Questions on HCF of 158, 9756, 5105 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 158, 9756, 5105?
Answer: HCF of 158, 9756, 5105 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 158, 9756, 5105 using Euclid's Algorithm?
Answer: For arbitrary numbers 158, 9756, 5105 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.