Highest Common Factor of 360, 617, 332 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 360, 617, 332 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 360, 617, 332 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 360, 617, 332 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 360, 617, 332 is 1.
HCF(360, 617, 332) = 1
HCF of 360, 617, 332 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 360, 617, 332 is 1.
Highest Common Factor of 360,617,332 is 1
Step 1: Since 617 > 360, we apply the division lemma to 617 and 360, to get
617 = 360 x 1 + 257
Step 2: Since the reminder 360 ≠ 0, we apply division lemma to 257 and 360, to get
360 = 257 x 1 + 103
Step 3: We consider the new divisor 257 and the new remainder 103, and apply the division lemma to get
257 = 103 x 2 + 51
We consider the new divisor 103 and the new remainder 51,and apply the division lemma to get
103 = 51 x 2 + 1
We consider the new divisor 51 and the new remainder 1,and apply the division lemma to get
51 = 1 x 51 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 360 and 617 is 1
Notice that 1 = HCF(51,1) = HCF(103,51) = HCF(257,103) = HCF(360,257) = HCF(617,360) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 332 > 1, we apply the division lemma to 332 and 1, to get
332 = 1 x 332 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 332 is 1
Notice that 1 = HCF(332,1) .
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Frequently Asked Questions on HCF of 360, 617, 332 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 360, 617, 332?
Answer: HCF of 360, 617, 332 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 360, 617, 332 using Euclid's Algorithm?
Answer: For arbitrary numbers 360, 617, 332 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.