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 874, 514, 311, 728 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 874, 514, 311, 728 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 874, 514, 311, 728 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 874, 514, 311, 728 is 1.
HCF(874, 514, 311, 728) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 874, 514, 311, 728 is 1.
Step 1: Since 874 > 514, we apply the division lemma to 874 and 514, to get
874 = 514 x 1 + 360
Step 2: Since the reminder 514 ≠ 0, we apply division lemma to 360 and 514, to get
514 = 360 x 1 + 154
Step 3: We consider the new divisor 360 and the new remainder 154, and apply the division lemma to get
360 = 154 x 2 + 52
We consider the new divisor 154 and the new remainder 52,and apply the division lemma to get
154 = 52 x 2 + 50
We consider the new divisor 52 and the new remainder 50,and apply the division lemma to get
52 = 50 x 1 + 2
We consider the new divisor 50 and the new remainder 2,and apply the division lemma to get
50 = 2 x 25 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 874 and 514 is 2
Notice that 2 = HCF(50,2) = HCF(52,50) = HCF(154,52) = HCF(360,154) = HCF(514,360) = HCF(874,514) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 311 > 2, we apply the division lemma to 311 and 2, to get
311 = 2 x 155 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 311 is 1
Notice that 1 = HCF(2,1) = HCF(311,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 728 > 1, we apply the division lemma to 728 and 1, to get
728 = 1 x 728 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 728 is 1
Notice that 1 = HCF(728,1) .
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 874, 514, 311, 728?
Answer: HCF of 874, 514, 311, 728 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 874, 514, 311, 728 using Euclid's Algorithm?
Answer: For arbitrary numbers 874, 514, 311, 728 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.