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 537, 838, 68 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 537, 838, 68 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 537, 838, 68 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 537, 838, 68 is 1.
HCF(537, 838, 68) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 537, 838, 68 is 1.
Step 1: Since 838 > 537, we apply the division lemma to 838 and 537, to get
838 = 537 x 1 + 301
Step 2: Since the reminder 537 ≠ 0, we apply division lemma to 301 and 537, to get
537 = 301 x 1 + 236
Step 3: We consider the new divisor 301 and the new remainder 236, and apply the division lemma to get
301 = 236 x 1 + 65
We consider the new divisor 236 and the new remainder 65,and apply the division lemma to get
236 = 65 x 3 + 41
We consider the new divisor 65 and the new remainder 41,and apply the division lemma to get
65 = 41 x 1 + 24
We consider the new divisor 41 and the new remainder 24,and apply the division lemma to get
41 = 24 x 1 + 17
We consider the new divisor 24 and the new remainder 17,and apply the division lemma to get
24 = 17 x 1 + 7
We consider the new divisor 17 and the new remainder 7,and apply the division lemma to get
17 = 7 x 2 + 3
We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get
7 = 3 x 2 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 537 and 838 is 1
Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(17,7) = HCF(24,17) = HCF(41,24) = HCF(65,41) = HCF(236,65) = HCF(301,236) = HCF(537,301) = HCF(838,537) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 68 > 1, we apply the division lemma to 68 and 1, to get
68 = 1 x 68 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 68 is 1
Notice that 1 = HCF(68,1) .
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 537, 838, 68?
Answer: HCF of 537, 838, 68 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 537, 838, 68 using Euclid's Algorithm?
Answer: For arbitrary numbers 537, 838, 68 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.