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 345, 812, 797 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 345, 812, 797 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 345, 812, 797 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 345, 812, 797 is 1.
HCF(345, 812, 797) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 345, 812, 797 is 1.
Step 1: Since 812 > 345, we apply the division lemma to 812 and 345, to get
812 = 345 x 2 + 122
Step 2: Since the reminder 345 ≠ 0, we apply division lemma to 122 and 345, to get
345 = 122 x 2 + 101
Step 3: We consider the new divisor 122 and the new remainder 101, and apply the division lemma to get
122 = 101 x 1 + 21
We consider the new divisor 101 and the new remainder 21,and apply the division lemma to get
101 = 21 x 4 + 17
We consider the new divisor 21 and the new remainder 17,and apply the division lemma to get
21 = 17 x 1 + 4
We consider the new divisor 17 and the new remainder 4,and apply the division lemma to get
17 = 4 x 4 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 345 and 812 is 1
Notice that 1 = HCF(4,1) = HCF(17,4) = HCF(21,17) = HCF(101,21) = HCF(122,101) = HCF(345,122) = HCF(812,345) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 797 > 1, we apply the division lemma to 797 and 1, to get
797 = 1 x 797 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 797 is 1
Notice that 1 = HCF(797,1) .
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 345, 812, 797?
Answer: HCF of 345, 812, 797 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 345, 812, 797 using Euclid's Algorithm?
Answer: For arbitrary numbers 345, 812, 797 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.