Highest Common Factor of 76, 130 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 76, 130 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 76, 130 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 76, 130 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 76, 130 is 2.
HCF(76, 130) = 2
HCF of 76, 130 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 76, 130 is 2.
Highest Common Factor of 76,130 is 2
Step 1: Since 130 > 76, we apply the division lemma to 130 and 76, to get
130 = 76 x 1 + 54
Step 2: Since the reminder 76 ≠ 0, we apply division lemma to 54 and 76, to get
76 = 54 x 1 + 22
Step 3: We consider the new divisor 54 and the new remainder 22, and apply the division lemma to get
54 = 22 x 2 + 10
We consider the new divisor 22 and the new remainder 10,and apply the division lemma to get
22 = 10 x 2 + 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 76 and 130 is 2
Notice that 2 = HCF(10,2) = HCF(22,10) = HCF(54,22) = HCF(76,54) = HCF(130,76) .
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Frequently Asked Questions on HCF of 76, 130 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 76, 130?
Answer: HCF of 76, 130 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 76, 130 using Euclid's Algorithm?
Answer: For arbitrary numbers 76, 130 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.