Highest Common Factor of 691, 401 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 691, 401 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 691, 401 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 691, 401 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 691, 401 is 1.
HCF(691, 401) = 1
HCF of 691, 401 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 691, 401 is 1.
Highest Common Factor of 691,401 is 1
Step 1: Since 691 > 401, we apply the division lemma to 691 and 401, to get
691 = 401 x 1 + 290
Step 2: Since the reminder 401 ≠ 0, we apply division lemma to 290 and 401, to get
401 = 290 x 1 + 111
Step 3: We consider the new divisor 290 and the new remainder 111, and apply the division lemma to get
290 = 111 x 2 + 68
We consider the new divisor 111 and the new remainder 68,and apply the division lemma to get
111 = 68 x 1 + 43
We consider the new divisor 68 and the new remainder 43,and apply the division lemma to get
68 = 43 x 1 + 25
We consider the new divisor 43 and the new remainder 25,and apply the division lemma to get
43 = 25 x 1 + 18
We consider the new divisor 25 and the new remainder 18,and apply the division lemma to get
25 = 18 x 1 + 7
We consider the new divisor 18 and the new remainder 7,and apply the division lemma to get
18 = 7 x 2 + 4
We consider the new divisor 7 and the new remainder 4,and apply the division lemma to get
7 = 4 x 1 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 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 691 and 401 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(18,7) = HCF(25,18) = HCF(43,25) = HCF(68,43) = HCF(111,68) = HCF(290,111) = HCF(401,290) = HCF(691,401) .
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Frequently Asked Questions on HCF of 691, 401 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 691, 401?
Answer: HCF of 691, 401 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 691, 401 using Euclid's Algorithm?
Answer: For arbitrary numbers 691, 401 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.