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, 948, 827, 32 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 627, 948, 827, 32 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 627, 948, 827, 32 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, 948, 827, 32 is 1.
HCF(627, 948, 827, 32) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 627, 948, 827, 32 is 1.
Step 1: Since 948 > 627, we apply the division lemma to 948 and 627, to get
948 = 627 x 1 + 321
Step 2: Since the reminder 627 ≠ 0, we apply division lemma to 321 and 627, to get
627 = 321 x 1 + 306
Step 3: We consider the new divisor 321 and the new remainder 306, and apply the division lemma to get
321 = 306 x 1 + 15
We consider the new divisor 306 and the new remainder 15,and apply the division lemma to get
306 = 15 x 20 + 6
We consider the new divisor 15 and the new remainder 6,and apply the division lemma to get
15 = 6 x 2 + 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 948 is 3
Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(306,15) = HCF(321,306) = HCF(627,321) = HCF(948,627) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 827 > 3, we apply the division lemma to 827 and 3, to get
827 = 3 x 275 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: 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 3 and 827 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(827,3) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 32 > 1, we apply the division lemma to 32 and 1, to get
32 = 1 x 32 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 32 is 1
Notice that 1 = HCF(32,1) .
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 627, 948, 827, 32?
Answer: HCF of 627, 948, 827, 32 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 627, 948, 827, 32 using Euclid's Algorithm?
Answer: For arbitrary numbers 627, 948, 827, 32 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.