Highest Common Factor of 266, 1340 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 266, 1340 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 266, 1340 is 2 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 266, 1340 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 266, 1340 is 2.
HCF(266, 1340) = 2
HCF of 266, 1340 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 266, 1340 is 2.
Highest Common Factor of 266,1340 is 2
Step 1: Since 1340 > 266, we apply the division lemma to 1340 and 266, to get
1340 = 266 x 5 + 10
Step 2: Since the reminder 266 ≠ 0, we apply division lemma to 10 and 266, to get
266 = 10 x 26 + 6
Step 3: We consider the new divisor 10 and the new remainder 6, and apply the division lemma to get
10 = 6 x 1 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 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 266 and 1340 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(266,10) = HCF(1340,266) .
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Frequently Asked Questions on HCF of 266, 1340 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 266, 1340?
Answer: HCF of 266, 1340 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 266, 1340 using Euclid's Algorithm?
Answer: For arbitrary numbers 266, 1340 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.