Highest Common Factor of 663, 272, 360 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 663, 272, 360 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 663, 272, 360 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 663, 272, 360 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 663, 272, 360 is 1.
HCF(663, 272, 360) = 1
HCF of 663, 272, 360 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 663, 272, 360 is 1.
Highest Common Factor of 663,272,360 is 1
Step 1: Since 663 > 272, we apply the division lemma to 663 and 272, to get
663 = 272 x 2 + 119
Step 2: Since the reminder 272 ≠ 0, we apply division lemma to 119 and 272, to get
272 = 119 x 2 + 34
Step 3: We consider the new divisor 119 and the new remainder 34, and apply the division lemma to get
119 = 34 x 3 + 17
We consider the new divisor 34 and the new remainder 17, and apply the division lemma to get
34 = 17 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 17, the HCF of 663 and 272 is 17
Notice that 17 = HCF(34,17) = HCF(119,34) = HCF(272,119) = HCF(663,272) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 360 > 17, we apply the division lemma to 360 and 17, to get
360 = 17 x 21 + 3
Step 2: Since the reminder 17 ≠ 0, we apply division lemma to 3 and 17, to get
17 = 3 x 5 + 2
Step 3: We consider the new divisor 3 and the new remainder 2, and apply the division lemma to get
3 = 2 x 1 + 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 17 and 360 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(17,3) = HCF(360,17) .
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Frequently Asked Questions on HCF of 663, 272, 360 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 663, 272, 360?
Answer: HCF of 663, 272, 360 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 663, 272, 360 using Euclid's Algorithm?
Answer: For arbitrary numbers 663, 272, 360 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
