Highest Common Factor of 1745, 5961 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 1745, 5961 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 1745, 5961 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 1745, 5961 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 1745, 5961 is 1.
HCF(1745, 5961) = 1
HCF of 1745, 5961 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1745, 5961 is 1.
Highest Common Factor of 1745,5961 is 1
Step 1: Since 5961 > 1745, we apply the division lemma to 5961 and 1745, to get
5961 = 1745 x 3 + 726
Step 2: Since the reminder 1745 ≠ 0, we apply division lemma to 726 and 1745, to get
1745 = 726 x 2 + 293
Step 3: We consider the new divisor 726 and the new remainder 293, and apply the division lemma to get
726 = 293 x 2 + 140
We consider the new divisor 293 and the new remainder 140,and apply the division lemma to get
293 = 140 x 2 + 13
We consider the new divisor 140 and the new remainder 13,and apply the division lemma to get
140 = 13 x 10 + 10
We consider the new divisor 13 and the new remainder 10,and apply the division lemma to get
13 = 10 x 1 + 3
We consider the new divisor 10 and the new remainder 3,and apply the division lemma to get
10 = 3 x 3 + 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 1745 and 5961 is 1
Notice that 1 = HCF(3,1) = HCF(10,3) = HCF(13,10) = HCF(140,13) = HCF(293,140) = HCF(726,293) = HCF(1745,726) = HCF(5961,1745) .
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Frequently Asked Questions on HCF of 1745, 5961 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 1745, 5961?
Answer: HCF of 1745, 5961 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1745, 5961 using Euclid's Algorithm?
Answer: For arbitrary numbers 1745, 5961 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.