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 728, 558, 37 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 728, 558, 37 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 728, 558, 37 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 728, 558, 37 is 1.
HCF(728, 558, 37) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 728, 558, 37 is 1.
Step 1: Since 728 > 558, we apply the division lemma to 728 and 558, to get
728 = 558 x 1 + 170
Step 2: Since the reminder 558 ≠ 0, we apply division lemma to 170 and 558, to get
558 = 170 x 3 + 48
Step 3: We consider the new divisor 170 and the new remainder 48, and apply the division lemma to get
170 = 48 x 3 + 26
We consider the new divisor 48 and the new remainder 26,and apply the division lemma to get
48 = 26 x 1 + 22
We consider the new divisor 26 and the new remainder 22,and apply the division lemma to get
26 = 22 x 1 + 4
We consider the new divisor 22 and the new remainder 4,and apply the division lemma to get
22 = 4 x 5 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 728 and 558 is 2
Notice that 2 = HCF(4,2) = HCF(22,4) = HCF(26,22) = HCF(48,26) = HCF(170,48) = HCF(558,170) = HCF(728,558) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 37 > 2, we apply the division lemma to 37 and 2, to get
37 = 2 x 18 + 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 37 is 1
Notice that 1 = HCF(2,1) = HCF(37,2) .
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 728, 558, 37?
Answer: HCF of 728, 558, 37 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 728, 558, 37 using Euclid's Algorithm?
Answer: For arbitrary numbers 728, 558, 37 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.