Highest Common Factor of 276, 657, 180 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 276, 657, 180 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 276, 657, 180 is 3 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 276, 657, 180 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 276, 657, 180 is 3.
HCF(276, 657, 180) = 3
HCF of 276, 657, 180 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 276, 657, 180 is 3.
Highest Common Factor of 276,657,180 is 3
Step 1: Since 657 > 276, we apply the division lemma to 657 and 276, to get
657 = 276 x 2 + 105
Step 2: Since the reminder 276 ≠ 0, we apply division lemma to 105 and 276, to get
276 = 105 x 2 + 66
Step 3: We consider the new divisor 105 and the new remainder 66, and apply the division lemma to get
105 = 66 x 1 + 39
We consider the new divisor 66 and the new remainder 39,and apply the division lemma to get
66 = 39 x 1 + 27
We consider the new divisor 39 and the new remainder 27,and apply the division lemma to get
39 = 27 x 1 + 12
We consider the new divisor 27 and the new remainder 12,and apply the division lemma to get
27 = 12 x 2 + 3
We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 276 and 657 is 3
Notice that 3 = HCF(12,3) = HCF(27,12) = HCF(39,27) = HCF(66,39) = HCF(105,66) = HCF(276,105) = HCF(657,276) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 180 > 3, we apply the division lemma to 180 and 3, to get
180 = 3 x 60 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 180 is 3
Notice that 3 = HCF(180,3) .
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Frequently Asked Questions on HCF of 276, 657, 180 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 276, 657, 180?
Answer: HCF of 276, 657, 180 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 276, 657, 180 using Euclid's Algorithm?
Answer: For arbitrary numbers 276, 657, 180 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.