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 27, 216, 684 i.e. 9 the largest integer that leaves a remainder zero for all numbers.
HCF of 27, 216, 684 is 9 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 27, 216, 684 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 27, 216, 684 is 9.
HCF(27, 216, 684) = 9
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 27, 216, 684 is 9.
Step 1: Since 216 > 27, we apply the division lemma to 216 and 27, to get
216 = 27 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 27, the HCF of 27 and 216 is 27
Notice that 27 = HCF(216,27) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 684 > 27, we apply the division lemma to 684 and 27, to get
684 = 27 x 25 + 9
Step 2: Since the reminder 27 ≠ 0, we apply division lemma to 9 and 27, to get
27 = 9 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 27 and 684 is 9
Notice that 9 = HCF(27,9) = HCF(684,27) .
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 27, 216, 684?
Answer: HCF of 27, 216, 684 is 9 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 27, 216, 684 using Euclid's Algorithm?
Answer: For arbitrary numbers 27, 216, 684 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.