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 744, 539, 874 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 744, 539, 874 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 744, 539, 874 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 744, 539, 874 is 1.
HCF(744, 539, 874) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 744, 539, 874 is 1.
Step 1: Since 744 > 539, we apply the division lemma to 744 and 539, to get
744 = 539 x 1 + 205
Step 2: Since the reminder 539 ≠ 0, we apply division lemma to 205 and 539, to get
539 = 205 x 2 + 129
Step 3: We consider the new divisor 205 and the new remainder 129, and apply the division lemma to get
205 = 129 x 1 + 76
We consider the new divisor 129 and the new remainder 76,and apply the division lemma to get
129 = 76 x 1 + 53
We consider the new divisor 76 and the new remainder 53,and apply the division lemma to get
76 = 53 x 1 + 23
We consider the new divisor 53 and the new remainder 23,and apply the division lemma to get
53 = 23 x 2 + 7
We consider the new divisor 23 and the new remainder 7,and apply the division lemma to get
23 = 7 x 3 + 2
We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get
7 = 2 x 3 + 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 744 and 539 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(23,7) = HCF(53,23) = HCF(76,53) = HCF(129,76) = HCF(205,129) = HCF(539,205) = HCF(744,539) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 874 > 1, we apply the division lemma to 874 and 1, to get
874 = 1 x 874 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 874 is 1
Notice that 1 = HCF(874,1) .
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 744, 539, 874?
Answer: HCF of 744, 539, 874 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 744, 539, 874 using Euclid's Algorithm?
Answer: For arbitrary numbers 744, 539, 874 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.