Highest Common Factor of 371, 642, 133 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 371, 642, 133 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 371, 642, 133 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 371, 642, 133 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 371, 642, 133 is 1.
HCF(371, 642, 133) = 1
HCF of 371, 642, 133 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 371, 642, 133 is 1.
Highest Common Factor of 371,642,133 is 1
Step 1: Since 642 > 371, we apply the division lemma to 642 and 371, to get
642 = 371 x 1 + 271
Step 2: Since the reminder 371 ≠ 0, we apply division lemma to 271 and 371, to get
371 = 271 x 1 + 100
Step 3: We consider the new divisor 271 and the new remainder 100, and apply the division lemma to get
271 = 100 x 2 + 71
We consider the new divisor 100 and the new remainder 71,and apply the division lemma to get
100 = 71 x 1 + 29
We consider the new divisor 71 and the new remainder 29,and apply the division lemma to get
71 = 29 x 2 + 13
We consider the new divisor 29 and the new remainder 13,and apply the division lemma to get
29 = 13 x 2 + 3
We consider the new divisor 13 and the new remainder 3,and apply the division lemma to get
13 = 3 x 4 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 371 and 642 is 1
Notice that 1 = HCF(3,1) = HCF(13,3) = HCF(29,13) = HCF(71,29) = HCF(100,71) = HCF(271,100) = HCF(371,271) = HCF(642,371) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 133 > 1, we apply the division lemma to 133 and 1, to get
133 = 1 x 133 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 133 is 1
Notice that 1 = HCF(133,1) .
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Frequently Asked Questions on HCF of 371, 642, 133 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 371, 642, 133?
Answer: HCF of 371, 642, 133 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 371, 642, 133 using Euclid's Algorithm?
Answer: For arbitrary numbers 371, 642, 133 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
