Highest Common Factor of 268, 710, 145 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 268, 710, 145 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 268, 710, 145 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 268, 710, 145 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 268, 710, 145 is 1.
HCF(268, 710, 145) = 1
HCF of 268, 710, 145 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 268, 710, 145 is 1.
Highest Common Factor of 268,710,145 is 1
Step 1: Since 710 > 268, we apply the division lemma to 710 and 268, to get
710 = 268 x 2 + 174
Step 2: Since the reminder 268 ≠ 0, we apply division lemma to 174 and 268, to get
268 = 174 x 1 + 94
Step 3: We consider the new divisor 174 and the new remainder 94, and apply the division lemma to get
174 = 94 x 1 + 80
We consider the new divisor 94 and the new remainder 80,and apply the division lemma to get
94 = 80 x 1 + 14
We consider the new divisor 80 and the new remainder 14,and apply the division lemma to get
80 = 14 x 5 + 10
We consider the new divisor 14 and the new remainder 10,and apply the division lemma to get
14 = 10 x 1 + 4
We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get
10 = 4 x 2 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 268 and 710 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(14,10) = HCF(80,14) = HCF(94,80) = HCF(174,94) = HCF(268,174) = HCF(710,268) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 145 > 2, we apply the division lemma to 145 and 2, to get
145 = 2 x 72 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 145 is 1
Notice that 1 = HCF(2,1) = HCF(145,2) .
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Frequently Asked Questions on HCF of 268, 710, 145 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 268, 710, 145?
Answer: HCF of 268, 710, 145 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 268, 710, 145 using Euclid's Algorithm?
Answer: For arbitrary numbers 268, 710, 145 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.