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, 467, 309 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 861, 467, 309 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, 467, 309 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, 467, 309 is 1.
HCF(861, 467, 309) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 861, 467, 309 is 1.
Step 1: Since 861 > 467, we apply the division lemma to 861 and 467, to get
861 = 467 x 1 + 394
Step 2: Since the reminder 467 ≠ 0, we apply division lemma to 394 and 467, to get
467 = 394 x 1 + 73
Step 3: We consider the new divisor 394 and the new remainder 73, and apply the division lemma to get
394 = 73 x 5 + 29
We consider the new divisor 73 and the new remainder 29,and apply the division lemma to get
73 = 29 x 2 + 15
We consider the new divisor 29 and the new remainder 15,and apply the division lemma to get
29 = 15 x 1 + 14
We consider the new divisor 15 and the new remainder 14,and apply the division lemma to get
15 = 14 x 1 + 1
We consider the new divisor 14 and the new remainder 1,and apply the division lemma to get
14 = 1 x 14 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 861 and 467 is 1
Notice that 1 = HCF(14,1) = HCF(15,14) = HCF(29,15) = HCF(73,29) = HCF(394,73) = HCF(467,394) = HCF(861,467) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 309 > 1, we apply the division lemma to 309 and 1, to get
309 = 1 x 309 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 309 is 1
Notice that 1 = HCF(309,1) .
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 861, 467, 309?
Answer: HCF of 861, 467, 309 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 861, 467, 309 using Euclid's Algorithm?
Answer: For arbitrary numbers 861, 467, 309 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.