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 627, 984, 159 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 627, 984, 159 is 3 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 627, 984, 159 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 627, 984, 159 is 3.
HCF(627, 984, 159) = 3
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 627, 984, 159 is 3.
Step 1: Since 984 > 627, we apply the division lemma to 984 and 627, to get
984 = 627 x 1 + 357
Step 2: Since the reminder 627 ≠ 0, we apply division lemma to 357 and 627, to get
627 = 357 x 1 + 270
Step 3: We consider the new divisor 357 and the new remainder 270, and apply the division lemma to get
357 = 270 x 1 + 87
We consider the new divisor 270 and the new remainder 87,and apply the division lemma to get
270 = 87 x 3 + 9
We consider the new divisor 87 and the new remainder 9,and apply the division lemma to get
87 = 9 x 9 + 6
We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get
9 = 6 x 1 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 627 and 984 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(87,9) = HCF(270,87) = HCF(357,270) = HCF(627,357) = HCF(984,627) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 159 > 3, we apply the division lemma to 159 and 3, to get
159 = 3 x 53 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 159 is 3
Notice that 3 = HCF(159,3) .
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 627, 984, 159?
Answer: HCF of 627, 984, 159 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 627, 984, 159 using Euclid's Algorithm?
Answer: For arbitrary numbers 627, 984, 159 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.