Highest Common Factor of 683, 260, 114 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 683, 260, 114 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 683, 260, 114 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 683, 260, 114 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 683, 260, 114 is 1.
HCF(683, 260, 114) = 1
HCF of 683, 260, 114 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 683, 260, 114 is 1.
Highest Common Factor of 683,260,114 is 1
Step 1: Since 683 > 260, we apply the division lemma to 683 and 260, to get
683 = 260 x 2 + 163
Step 2: Since the reminder 260 ≠ 0, we apply division lemma to 163 and 260, to get
260 = 163 x 1 + 97
Step 3: We consider the new divisor 163 and the new remainder 97, and apply the division lemma to get
163 = 97 x 1 + 66
We consider the new divisor 97 and the new remainder 66,and apply the division lemma to get
97 = 66 x 1 + 31
We consider the new divisor 66 and the new remainder 31,and apply the division lemma to get
66 = 31 x 2 + 4
We consider the new divisor 31 and the new remainder 4,and apply the division lemma to get
31 = 4 x 7 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 683 and 260 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(31,4) = HCF(66,31) = HCF(97,66) = HCF(163,97) = HCF(260,163) = HCF(683,260) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 114 > 1, we apply the division lemma to 114 and 1, to get
114 = 1 x 114 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 114 is 1
Notice that 1 = HCF(114,1) .
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Frequently Asked Questions on HCF of 683, 260, 114 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 683, 260, 114?
Answer: HCF of 683, 260, 114 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 683, 260, 114 using Euclid's Algorithm?
Answer: For arbitrary numbers 683, 260, 114 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.