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 812, 505, 585, 24 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 812, 505, 585, 24 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 812, 505, 585, 24 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 812, 505, 585, 24 is 1.
HCF(812, 505, 585, 24) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 812, 505, 585, 24 is 1.
Step 1: Since 812 > 505, we apply the division lemma to 812 and 505, to get
812 = 505 x 1 + 307
Step 2: Since the reminder 505 ≠ 0, we apply division lemma to 307 and 505, to get
505 = 307 x 1 + 198
Step 3: We consider the new divisor 307 and the new remainder 198, and apply the division lemma to get
307 = 198 x 1 + 109
We consider the new divisor 198 and the new remainder 109,and apply the division lemma to get
198 = 109 x 1 + 89
We consider the new divisor 109 and the new remainder 89,and apply the division lemma to get
109 = 89 x 1 + 20
We consider the new divisor 89 and the new remainder 20,and apply the division lemma to get
89 = 20 x 4 + 9
We consider the new divisor 20 and the new remainder 9,and apply the division lemma to get
20 = 9 x 2 + 2
We consider the new divisor 9 and the new remainder 2,and apply the division lemma to get
9 = 2 x 4 + 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 812 and 505 is 1
Notice that 1 = HCF(2,1) = HCF(9,2) = HCF(20,9) = HCF(89,20) = HCF(109,89) = HCF(198,109) = HCF(307,198) = HCF(505,307) = HCF(812,505) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 585 > 1, we apply the division lemma to 585 and 1, to get
585 = 1 x 585 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 585 is 1
Notice that 1 = HCF(585,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 24 > 1, we apply the division lemma to 24 and 1, to get
24 = 1 x 24 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 24 is 1
Notice that 1 = HCF(24,1) .
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 812, 505, 585, 24?
Answer: HCF of 812, 505, 585, 24 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 812, 505, 585, 24 using Euclid's Algorithm?
Answer: For arbitrary numbers 812, 505, 585, 24 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.