Highest Common Factor of 130, 305, 76 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, 305, 76 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 130, 305, 76 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 130, 305, 76 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, 305, 76 is 1.
HCF(130, 305, 76) = 1
HCF of 130, 305, 76 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, 305, 76 is 1.
Highest Common Factor of 130,305,76 is 1
Step 1: Since 305 > 130, we apply the division lemma to 305 and 130, to get
305 = 130 x 2 + 45
Step 2: Since the reminder 130 ≠ 0, we apply division lemma to 45 and 130, to get
130 = 45 x 2 + 40
Step 3: We consider the new divisor 45 and the new remainder 40, and apply the division lemma to get
45 = 40 x 1 + 5
We consider the new divisor 40 and the new remainder 5, and apply the division lemma to get
40 = 5 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 130 and 305 is 5
Notice that 5 = HCF(40,5) = HCF(45,40) = HCF(130,45) = HCF(305,130) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 76 > 5, we apply the division lemma to 76 and 5, to get
76 = 5 x 15 + 1
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 1 and 5, to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5 and 76 is 1
Notice that 1 = HCF(5,1) = HCF(76,5) .
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Frequently Asked Questions on HCF of 130, 305, 76 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, 305, 76?
Answer: HCF of 130, 305, 76 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 130, 305, 76 using Euclid's Algorithm?
Answer: For arbitrary numbers 130, 305, 76 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.