Highest Common Factor of 129, 316, 75 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 129, 316, 75 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 129, 316, 75 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 129, 316, 75 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 129, 316, 75 is 1.
HCF(129, 316, 75) = 1
HCF of 129, 316, 75 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 129, 316, 75 is 1.
Highest Common Factor of 129,316,75 is 1
Step 1: Since 316 > 129, we apply the division lemma to 316 and 129, to get
316 = 129 x 2 + 58
Step 2: Since the reminder 129 ≠ 0, we apply division lemma to 58 and 129, to get
129 = 58 x 2 + 13
Step 3: We consider the new divisor 58 and the new remainder 13, and apply the division lemma to get
58 = 13 x 4 + 6
We consider the new divisor 13 and the new remainder 6,and apply the division lemma to get
13 = 6 x 2 + 1
We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 129 and 316 is 1
Notice that 1 = HCF(6,1) = HCF(13,6) = HCF(58,13) = HCF(129,58) = HCF(316,129) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 75 > 1, we apply the division lemma to 75 and 1, to get
75 = 1 x 75 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 75 is 1
Notice that 1 = HCF(75,1) .
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Frequently Asked Questions on HCF of 129, 316, 75 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 129, 316, 75?
Answer: HCF of 129, 316, 75 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 129, 316, 75 using Euclid's Algorithm?
Answer: For arbitrary numbers 129, 316, 75 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.