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 291, 405, 812 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 291, 405, 812 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 291, 405, 812 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 291, 405, 812 is 1.
HCF(291, 405, 812) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 291, 405, 812 is 1.
Step 1: Since 405 > 291, we apply the division lemma to 405 and 291, to get
405 = 291 x 1 + 114
Step 2: Since the reminder 291 ≠ 0, we apply division lemma to 114 and 291, to get
291 = 114 x 2 + 63
Step 3: We consider the new divisor 114 and the new remainder 63, and apply the division lemma to get
114 = 63 x 1 + 51
We consider the new divisor 63 and the new remainder 51,and apply the division lemma to get
63 = 51 x 1 + 12
We consider the new divisor 51 and the new remainder 12,and apply the division lemma to get
51 = 12 x 4 + 3
We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 291 and 405 is 3
Notice that 3 = HCF(12,3) = HCF(51,12) = HCF(63,51) = HCF(114,63) = HCF(291,114) = HCF(405,291) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 812 > 3, we apply the division lemma to 812 and 3, to get
812 = 3 x 270 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: 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 3 and 812 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(812,3) .
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 291, 405, 812?
Answer: HCF of 291, 405, 812 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 291, 405, 812 using Euclid's Algorithm?
Answer: For arbitrary numbers 291, 405, 812 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.