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 869, 546, 461 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 869, 546, 461 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 869, 546, 461 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 869, 546, 461 is 1.
HCF(869, 546, 461) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 869, 546, 461 is 1.
Step 1: Since 869 > 546, we apply the division lemma to 869 and 546, to get
869 = 546 x 1 + 323
Step 2: Since the reminder 546 ≠ 0, we apply division lemma to 323 and 546, to get
546 = 323 x 1 + 223
Step 3: We consider the new divisor 323 and the new remainder 223, and apply the division lemma to get
323 = 223 x 1 + 100
We consider the new divisor 223 and the new remainder 100,and apply the division lemma to get
223 = 100 x 2 + 23
We consider the new divisor 100 and the new remainder 23,and apply the division lemma to get
100 = 23 x 4 + 8
We consider the new divisor 23 and the new remainder 8,and apply the division lemma to get
23 = 8 x 2 + 7
We consider the new divisor 8 and the new remainder 7,and apply the division lemma to get
8 = 7 x 1 + 1
We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 869 and 546 is 1
Notice that 1 = HCF(7,1) = HCF(8,7) = HCF(23,8) = HCF(100,23) = HCF(223,100) = HCF(323,223) = HCF(546,323) = HCF(869,546) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 461 > 1, we apply the division lemma to 461 and 1, to get
461 = 1 x 461 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 461 is 1
Notice that 1 = HCF(461,1) .
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 869, 546, 461?
Answer: HCF of 869, 546, 461 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 869, 546, 461 using Euclid's Algorithm?
Answer: For arbitrary numbers 869, 546, 461 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.