Highest Common Factor of 757, 2161 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 757, 2161 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 757, 2161 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 757, 2161 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 757, 2161 is 1.
HCF(757, 2161) = 1
HCF of 757, 2161 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 757, 2161 is 1.
Highest Common Factor of 757,2161 is 1
Step 1: Since 2161 > 757, we apply the division lemma to 2161 and 757, to get
2161 = 757 x 2 + 647
Step 2: Since the reminder 757 ≠ 0, we apply division lemma to 647 and 757, to get
757 = 647 x 1 + 110
Step 3: We consider the new divisor 647 and the new remainder 110, and apply the division lemma to get
647 = 110 x 5 + 97
We consider the new divisor 110 and the new remainder 97,and apply the division lemma to get
110 = 97 x 1 + 13
We consider the new divisor 97 and the new remainder 13,and apply the division lemma to get
97 = 13 x 7 + 6
We consider the new divisor 13 and the new remainder 6,and apply the division lemma to get
13 = 6 x 2 + 1
We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 757 and 2161 is 1
Notice that 1 = HCF(6,1) = HCF(13,6) = HCF(97,13) = HCF(110,97) = HCF(647,110) = HCF(757,647) = HCF(2161,757) .
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Frequently Asked Questions on HCF of 757, 2161 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 757, 2161?
Answer: HCF of 757, 2161 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 757, 2161 using Euclid's Algorithm?
Answer: For arbitrary numbers 757, 2161 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.