Highest Common Factor of 671, 366, 144 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 671, 366, 144 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 671, 366, 144 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 671, 366, 144 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 671, 366, 144 is 1.
HCF(671, 366, 144) = 1
HCF of 671, 366, 144 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 671, 366, 144 is 1.
Highest Common Factor of 671,366,144 is 1
Step 1: Since 671 > 366, we apply the division lemma to 671 and 366, to get
671 = 366 x 1 + 305
Step 2: Since the reminder 366 ≠ 0, we apply division lemma to 305 and 366, to get
366 = 305 x 1 + 61
Step 3: We consider the new divisor 305 and the new remainder 61, and apply the division lemma to get
305 = 61 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 61, the HCF of 671 and 366 is 61
Notice that 61 = HCF(305,61) = HCF(366,305) = HCF(671,366) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 144 > 61, we apply the division lemma to 144 and 61, to get
144 = 61 x 2 + 22
Step 2: Since the reminder 61 ≠ 0, we apply division lemma to 22 and 61, to get
61 = 22 x 2 + 17
Step 3: We consider the new divisor 22 and the new remainder 17, and apply the division lemma to get
22 = 17 x 1 + 5
We consider the new divisor 17 and the new remainder 5,and apply the division lemma to get
17 = 5 x 3 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 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 61 and 144 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(17,5) = HCF(22,17) = HCF(61,22) = HCF(144,61) .
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Frequently Asked Questions on HCF of 671, 366, 144 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 671, 366, 144?
Answer: HCF of 671, 366, 144 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 671, 366, 144 using Euclid's Algorithm?
Answer: For arbitrary numbers 671, 366, 144 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.