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 861, 609, 764 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 861, 609, 764 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 861, 609, 764 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 861, 609, 764 is 1.
HCF(861, 609, 764) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 861, 609, 764 is 1.
Step 1: Since 861 > 609, we apply the division lemma to 861 and 609, to get
861 = 609 x 1 + 252
Step 2: Since the reminder 609 ≠ 0, we apply division lemma to 252 and 609, to get
609 = 252 x 2 + 105
Step 3: We consider the new divisor 252 and the new remainder 105, and apply the division lemma to get
252 = 105 x 2 + 42
We consider the new divisor 105 and the new remainder 42,and apply the division lemma to get
105 = 42 x 2 + 21
We consider the new divisor 42 and the new remainder 21,and apply the division lemma to get
42 = 21 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 21, the HCF of 861 and 609 is 21
Notice that 21 = HCF(42,21) = HCF(105,42) = HCF(252,105) = HCF(609,252) = HCF(861,609) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 764 > 21, we apply the division lemma to 764 and 21, to get
764 = 21 x 36 + 8
Step 2: Since the reminder 21 ≠ 0, we apply division lemma to 8 and 21, to get
21 = 8 x 2 + 5
Step 3: We consider the new divisor 8 and the new remainder 5, and apply the division lemma to get
8 = 5 x 1 + 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 21 and 764 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(21,8) = HCF(764,21) .
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 861, 609, 764?
Answer: HCF of 861, 609, 764 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 861, 609, 764 using Euclid's Algorithm?
Answer: For arbitrary numbers 861, 609, 764 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.