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 561, 857, 785, 41 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 561, 857, 785, 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 561, 857, 785, 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 561, 857, 785, 41 is 1.
HCF(561, 857, 785, 41) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 561, 857, 785, 41 is 1.
Step 1: Since 857 > 561, we apply the division lemma to 857 and 561, to get
857 = 561 x 1 + 296
Step 2: Since the reminder 561 ≠ 0, we apply division lemma to 296 and 561, to get
561 = 296 x 1 + 265
Step 3: We consider the new divisor 296 and the new remainder 265, and apply the division lemma to get
296 = 265 x 1 + 31
We consider the new divisor 265 and the new remainder 31,and apply the division lemma to get
265 = 31 x 8 + 17
We consider the new divisor 31 and the new remainder 17,and apply the division lemma to get
31 = 17 x 1 + 14
We consider the new divisor 17 and the new remainder 14,and apply the division lemma to get
17 = 14 x 1 + 3
We consider the new divisor 14 and the new remainder 3,and apply the division lemma to get
14 = 3 x 4 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 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 561 and 857 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(14,3) = HCF(17,14) = HCF(31,17) = HCF(265,31) = HCF(296,265) = HCF(561,296) = HCF(857,561) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 785 > 1, we apply the division lemma to 785 and 1, to get
785 = 1 x 785 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 785 is 1
Notice that 1 = HCF(785,1) .
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 561, 857, 785, 41?
Answer: HCF of 561, 857, 785, 41 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 561, 857, 785, 41 using Euclid's Algorithm?
Answer: For arbitrary numbers 561, 857, 785, 41 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.