Highest Common Factor of 2097, 754 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 2097, 754 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 2097, 754 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 2097, 754 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 2097, 754 is 1.
HCF(2097, 754) = 1
HCF of 2097, 754 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2097, 754 is 1.
Highest Common Factor of 2097,754 is 1
Step 1: Since 2097 > 754, we apply the division lemma to 2097 and 754, to get
2097 = 754 x 2 + 589
Step 2: Since the reminder 754 ≠ 0, we apply division lemma to 589 and 754, to get
754 = 589 x 1 + 165
Step 3: We consider the new divisor 589 and the new remainder 165, and apply the division lemma to get
589 = 165 x 3 + 94
We consider the new divisor 165 and the new remainder 94,and apply the division lemma to get
165 = 94 x 1 + 71
We consider the new divisor 94 and the new remainder 71,and apply the division lemma to get
94 = 71 x 1 + 23
We consider the new divisor 71 and the new remainder 23,and apply the division lemma to get
71 = 23 x 3 + 2
We consider the new divisor 23 and the new remainder 2,and apply the division lemma to get
23 = 2 x 11 + 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 2097 and 754 is 1
Notice that 1 = HCF(2,1) = HCF(23,2) = HCF(71,23) = HCF(94,71) = HCF(165,94) = HCF(589,165) = HCF(754,589) = HCF(2097,754) .
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Frequently Asked Questions on HCF of 2097, 754 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 2097, 754?
Answer: HCF of 2097, 754 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2097, 754 using Euclid's Algorithm?
Answer: For arbitrary numbers 2097, 754 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.