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 80, 369, 691 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 80, 369, 691 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 80, 369, 691 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 80, 369, 691 is 1.
HCF(80, 369, 691) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 80, 369, 691 is 1.
Step 1: Since 369 > 80, we apply the division lemma to 369 and 80, to get
369 = 80 x 4 + 49
Step 2: Since the reminder 80 ≠ 0, we apply division lemma to 49 and 80, to get
80 = 49 x 1 + 31
Step 3: We consider the new divisor 49 and the new remainder 31, and apply the division lemma to get
49 = 31 x 1 + 18
We consider the new divisor 31 and the new remainder 18,and apply the division lemma to get
31 = 18 x 1 + 13
We consider the new divisor 18 and the new remainder 13,and apply the division lemma to get
18 = 13 x 1 + 5
We consider the new divisor 13 and the new remainder 5,and apply the division lemma to get
13 = 5 x 2 + 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 80 and 369 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(13,5) = HCF(18,13) = HCF(31,18) = HCF(49,31) = HCF(80,49) = HCF(369,80) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 691 > 1, we apply the division lemma to 691 and 1, to get
691 = 1 x 691 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 691 is 1
Notice that 1 = HCF(691,1) .
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 80, 369, 691?
Answer: HCF of 80, 369, 691 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 80, 369, 691 using Euclid's Algorithm?
Answer: For arbitrary numbers 80, 369, 691 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.