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 665, 820, 789 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 665, 820, 789 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 665, 820, 789 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 665, 820, 789 is 1.
HCF(665, 820, 789) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 665, 820, 789 is 1.
Step 1: Since 820 > 665, we apply the division lemma to 820 and 665, to get
820 = 665 x 1 + 155
Step 2: Since the reminder 665 ≠ 0, we apply division lemma to 155 and 665, to get
665 = 155 x 4 + 45
Step 3: We consider the new divisor 155 and the new remainder 45, and apply the division lemma to get
155 = 45 x 3 + 20
We consider the new divisor 45 and the new remainder 20,and apply the division lemma to get
45 = 20 x 2 + 5
We consider the new divisor 20 and the new remainder 5,and apply the division lemma to get
20 = 5 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 665 and 820 is 5
Notice that 5 = HCF(20,5) = HCF(45,20) = HCF(155,45) = HCF(665,155) = HCF(820,665) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 789 > 5, we apply the division lemma to 789 and 5, to get
789 = 5 x 157 + 4
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 4 and 5, to get
5 = 4 x 1 + 1
Step 3: 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 5 and 789 is 1
Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(789,5) .
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 665, 820, 789?
Answer: HCF of 665, 820, 789 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 665, 820, 789 using Euclid's Algorithm?
Answer: For arbitrary numbers 665, 820, 789 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.