Highest Common Factor of 660, 865, 113 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 660, 865, 113 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 660, 865, 113 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 660, 865, 113 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 660, 865, 113 is 1.
HCF(660, 865, 113) = 1
HCF of 660, 865, 113 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 660, 865, 113 is 1.
Highest Common Factor of 660,865,113 is 1
Step 1: Since 865 > 660, we apply the division lemma to 865 and 660, to get
865 = 660 x 1 + 205
Step 2: Since the reminder 660 ≠ 0, we apply division lemma to 205 and 660, to get
660 = 205 x 3 + 45
Step 3: We consider the new divisor 205 and the new remainder 45, and apply the division lemma to get
205 = 45 x 4 + 25
We consider the new divisor 45 and the new remainder 25,and apply the division lemma to get
45 = 25 x 1 + 20
We consider the new divisor 25 and the new remainder 20,and apply the division lemma to get
25 = 20 x 1 + 5
We consider the new divisor 20 and the new remainder 5,and apply the division lemma to get
20 = 5 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 660 and 865 is 5
Notice that 5 = HCF(20,5) = HCF(25,20) = HCF(45,25) = HCF(205,45) = HCF(660,205) = HCF(865,660) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 113 > 5, we apply the division lemma to 113 and 5, to get
113 = 5 x 22 + 3
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 3 and 5, to get
5 = 3 x 1 + 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 5 and 113 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(113,5) .
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Frequently Asked Questions on HCF of 660, 865, 113 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 660, 865, 113?
Answer: HCF of 660, 865, 113 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 660, 865, 113 using Euclid's Algorithm?
Answer: For arbitrary numbers 660, 865, 113 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
