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 678, 251, 327 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 678, 251, 327 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 678, 251, 327 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 678, 251, 327 is 1.
HCF(678, 251, 327) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 678, 251, 327 is 1.
Step 1: Since 678 > 251, we apply the division lemma to 678 and 251, to get
678 = 251 x 2 + 176
Step 2: Since the reminder 251 ≠ 0, we apply division lemma to 176 and 251, to get
251 = 176 x 1 + 75
Step 3: We consider the new divisor 176 and the new remainder 75, and apply the division lemma to get
176 = 75 x 2 + 26
We consider the new divisor 75 and the new remainder 26,and apply the division lemma to get
75 = 26 x 2 + 23
We consider the new divisor 26 and the new remainder 23,and apply the division lemma to get
26 = 23 x 1 + 3
We consider the new divisor 23 and the new remainder 3,and apply the division lemma to get
23 = 3 x 7 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
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 678 and 251 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(23,3) = HCF(26,23) = HCF(75,26) = HCF(176,75) = HCF(251,176) = HCF(678,251) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 327 > 1, we apply the division lemma to 327 and 1, to get
327 = 1 x 327 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 327 is 1
Notice that 1 = HCF(327,1) .
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 678, 251, 327?
Answer: HCF of 678, 251, 327 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 678, 251, 327 using Euclid's Algorithm?
Answer: For arbitrary numbers 678, 251, 327 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.