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 797, 309, 731 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 797, 309, 731 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 797, 309, 731 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 797, 309, 731 is 1.
HCF(797, 309, 731) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 797, 309, 731 is 1.
Step 1: Since 797 > 309, we apply the division lemma to 797 and 309, to get
797 = 309 x 2 + 179
Step 2: Since the reminder 309 ≠ 0, we apply division lemma to 179 and 309, to get
309 = 179 x 1 + 130
Step 3: We consider the new divisor 179 and the new remainder 130, and apply the division lemma to get
179 = 130 x 1 + 49
We consider the new divisor 130 and the new remainder 49,and apply the division lemma to get
130 = 49 x 2 + 32
We consider the new divisor 49 and the new remainder 32,and apply the division lemma to get
49 = 32 x 1 + 17
We consider the new divisor 32 and the new remainder 17,and apply the division lemma to get
32 = 17 x 1 + 15
We consider the new divisor 17 and the new remainder 15,and apply the division lemma to get
17 = 15 x 1 + 2
We consider the new divisor 15 and the new remainder 2,and apply the division lemma to get
15 = 2 x 7 + 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 797 and 309 is 1
Notice that 1 = HCF(2,1) = HCF(15,2) = HCF(17,15) = HCF(32,17) = HCF(49,32) = HCF(130,49) = HCF(179,130) = HCF(309,179) = HCF(797,309) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 731 > 1, we apply the division lemma to 731 and 1, to get
731 = 1 x 731 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 731 is 1
Notice that 1 = HCF(731,1) .
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 797, 309, 731?
Answer: HCF of 797, 309, 731 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 797, 309, 731 using Euclid's Algorithm?
Answer: For arbitrary numbers 797, 309, 731 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.