Highest Common Factor of 130, 75908 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 130, 75908 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 130, 75908 is 2 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 130, 75908 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 130, 75908 is 2.
HCF(130, 75908) = 2
HCF of 130, 75908 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 130, 75908 is 2.
Highest Common Factor of 130,75908 is 2
Step 1: Since 75908 > 130, we apply the division lemma to 75908 and 130, to get
75908 = 130 x 583 + 118
Step 2: Since the reminder 130 ≠ 0, we apply division lemma to 118 and 130, to get
130 = 118 x 1 + 12
Step 3: We consider the new divisor 118 and the new remainder 12, and apply the division lemma to get
118 = 12 x 9 + 10
We consider the new divisor 12 and the new remainder 10,and apply the division lemma to get
12 = 10 x 1 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 130 and 75908 is 2
Notice that 2 = HCF(10,2) = HCF(12,10) = HCF(118,12) = HCF(130,118) = HCF(75908,130) .
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Frequently Asked Questions on HCF of 130, 75908 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 130, 75908?
Answer: HCF of 130, 75908 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 130, 75908 using Euclid's Algorithm?
Answer: For arbitrary numbers 130, 75908 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.