Highest Common Factor of 373, 640, 71 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 373, 640, 71 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 373, 640, 71 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 373, 640, 71 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 373, 640, 71 is 1.
HCF(373, 640, 71) = 1
HCF of 373, 640, 71 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 373, 640, 71 is 1.
Highest Common Factor of 373,640,71 is 1
Step 1: Since 640 > 373, we apply the division lemma to 640 and 373, to get
640 = 373 x 1 + 267
Step 2: Since the reminder 373 ≠ 0, we apply division lemma to 267 and 373, to get
373 = 267 x 1 + 106
Step 3: We consider the new divisor 267 and the new remainder 106, and apply the division lemma to get
267 = 106 x 2 + 55
We consider the new divisor 106 and the new remainder 55,and apply the division lemma to get
106 = 55 x 1 + 51
We consider the new divisor 55 and the new remainder 51,and apply the division lemma to get
55 = 51 x 1 + 4
We consider the new divisor 51 and the new remainder 4,and apply the division lemma to get
51 = 4 x 12 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 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 373 and 640 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(51,4) = HCF(55,51) = HCF(106,55) = HCF(267,106) = HCF(373,267) = HCF(640,373) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 71 > 1, we apply the division lemma to 71 and 1, to get
71 = 1 x 71 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 71 is 1
Notice that 1 = HCF(71,1) .
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Frequently Asked Questions on HCF of 373, 640, 71 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 373, 640, 71?
Answer: HCF of 373, 640, 71 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 373, 640, 71 using Euclid's Algorithm?
Answer: For arbitrary numbers 373, 640, 71 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.