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 132, 303, 826, 41 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 132, 303, 826, 41 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 132, 303, 826, 41 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 132, 303, 826, 41 is 1.
HCF(132, 303, 826, 41) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 132, 303, 826, 41 is 1.
Step 1: Since 303 > 132, we apply the division lemma to 303 and 132, to get
303 = 132 x 2 + 39
Step 2: Since the reminder 132 ≠ 0, we apply division lemma to 39 and 132, to get
132 = 39 x 3 + 15
Step 3: We consider the new divisor 39 and the new remainder 15, and apply the division lemma to get
39 = 15 x 2 + 9
We consider the new divisor 15 and the new remainder 9,and apply the division lemma to get
15 = 9 x 1 + 6
We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get
9 = 6 x 1 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 132 and 303 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(15,9) = HCF(39,15) = HCF(132,39) = HCF(303,132) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 826 > 3, we apply the division lemma to 826 and 3, to get
826 = 3 x 275 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, 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 3 and 826 is 1
Notice that 1 = HCF(3,1) = HCF(826,3) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 41 > 1, we apply the division lemma to 41 and 1, to get
41 = 1 x 41 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 41 is 1
Notice that 1 = HCF(41,1) .
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 132, 303, 826, 41?
Answer: HCF of 132, 303, 826, 41 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 132, 303, 826, 41 using Euclid's Algorithm?
Answer: For arbitrary numbers 132, 303, 826, 41 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.