Highest Common Factor of 129, 74, 281 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, 74, 281 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 129, 74, 281 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, 74, 281 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, 74, 281 is 1.
HCF(129, 74, 281) = 1
HCF of 129, 74, 281 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, 74, 281 is 1.
Highest Common Factor of 129,74,281 is 1
Step 1: Since 129 > 74, we apply the division lemma to 129 and 74, to get
129 = 74 x 1 + 55
Step 2: Since the reminder 74 ≠ 0, we apply division lemma to 55 and 74, to get
74 = 55 x 1 + 19
Step 3: We consider the new divisor 55 and the new remainder 19, and apply the division lemma to get
55 = 19 x 2 + 17
We consider the new divisor 19 and the new remainder 17,and apply the division lemma to get
19 = 17 x 1 + 2
We consider the new divisor 17 and the new remainder 2,and apply the division lemma to get
17 = 2 x 8 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 129 and 74 is 1
Notice that 1 = HCF(2,1) = HCF(17,2) = HCF(19,17) = HCF(55,19) = HCF(74,55) = HCF(129,74) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 281 > 1, we apply the division lemma to 281 and 1, to get
281 = 1 x 281 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 281 is 1
Notice that 1 = HCF(281,1) .
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Frequently Asked Questions on HCF of 129, 74, 281 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, 74, 281?
Answer: HCF of 129, 74, 281 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 129, 74, 281 using Euclid's Algorithm?
Answer: For arbitrary numbers 129, 74, 281 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.