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 506, 720, 797 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 506, 720, 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 506, 720, 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 506, 720, 797 is 1.
HCF(506, 720, 797) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 506, 720, 797 is 1.
Step 1: Since 720 > 506, we apply the division lemma to 720 and 506, to get
720 = 506 x 1 + 214
Step 2: Since the reminder 506 ≠ 0, we apply division lemma to 214 and 506, to get
506 = 214 x 2 + 78
Step 3: We consider the new divisor 214 and the new remainder 78, and apply the division lemma to get
214 = 78 x 2 + 58
We consider the new divisor 78 and the new remainder 58,and apply the division lemma to get
78 = 58 x 1 + 20
We consider the new divisor 58 and the new remainder 20,and apply the division lemma to get
58 = 20 x 2 + 18
We consider the new divisor 20 and the new remainder 18,and apply the division lemma to get
20 = 18 x 1 + 2
We consider the new divisor 18 and the new remainder 2,and apply the division lemma to get
18 = 2 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 506 and 720 is 2
Notice that 2 = HCF(18,2) = HCF(20,18) = HCF(58,20) = HCF(78,58) = HCF(214,78) = HCF(506,214) = HCF(720,506) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 797 > 2, we apply the division lemma to 797 and 2, to get
797 = 2 x 398 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 797 is 1
Notice that 1 = HCF(2,1) = HCF(797,2) .
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 506, 720, 797?
Answer: HCF of 506, 720, 797 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 506, 720, 797 using Euclid's Algorithm?
Answer: For arbitrary numbers 506, 720, 797 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.