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 837, 529, 45 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 837, 529, 45 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 837, 529, 45 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 837, 529, 45 is 1.
HCF(837, 529, 45) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 837, 529, 45 is 1.
Step 1: Since 837 > 529, we apply the division lemma to 837 and 529, to get
837 = 529 x 1 + 308
Step 2: Since the reminder 529 ≠ 0, we apply division lemma to 308 and 529, to get
529 = 308 x 1 + 221
Step 3: We consider the new divisor 308 and the new remainder 221, and apply the division lemma to get
308 = 221 x 1 + 87
We consider the new divisor 221 and the new remainder 87,and apply the division lemma to get
221 = 87 x 2 + 47
We consider the new divisor 87 and the new remainder 47,and apply the division lemma to get
87 = 47 x 1 + 40
We consider the new divisor 47 and the new remainder 40,and apply the division lemma to get
47 = 40 x 1 + 7
We consider the new divisor 40 and the new remainder 7,and apply the division lemma to get
40 = 7 x 5 + 5
We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get
7 = 5 x 1 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 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 837 and 529 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(40,7) = HCF(47,40) = HCF(87,47) = HCF(221,87) = HCF(308,221) = HCF(529,308) = HCF(837,529) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 45 > 1, we apply the division lemma to 45 and 1, to get
45 = 1 x 45 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 45 is 1
Notice that 1 = HCF(45,1) .
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 837, 529, 45?
Answer: HCF of 837, 529, 45 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 837, 529, 45 using Euclid's Algorithm?
Answer: For arbitrary numbers 837, 529, 45 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.