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, 411, 692 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 691, 411, 692 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, 411, 692 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, 411, 692 is 1.
HCF(691, 411, 692) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 691, 411, 692 is 1.
Step 1: Since 691 > 411, we apply the division lemma to 691 and 411, to get
691 = 411 x 1 + 280
Step 2: Since the reminder 411 ≠ 0, we apply division lemma to 280 and 411, to get
411 = 280 x 1 + 131
Step 3: We consider the new divisor 280 and the new remainder 131, and apply the division lemma to get
280 = 131 x 2 + 18
We consider the new divisor 131 and the new remainder 18,and apply the division lemma to get
131 = 18 x 7 + 5
We consider the new divisor 18 and the new remainder 5,and apply the division lemma to get
18 = 5 x 3 + 3
We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get
5 = 3 x 1 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 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 691 and 411 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(18,5) = HCF(131,18) = HCF(280,131) = HCF(411,280) = HCF(691,411) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 692 > 1, we apply the division lemma to 692 and 1, to get
692 = 1 x 692 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 692 is 1
Notice that 1 = HCF(692,1) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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, 411, 692?
Answer: HCF of 691, 411, 692 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 691, 411, 692 using Euclid's Algorithm?
Answer: For arbitrary numbers 691, 411, 692 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.