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, 404, 718, 982 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 561, 404, 718, 982 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, 404, 718, 982 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, 404, 718, 982 is 1.
HCF(561, 404, 718, 982) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 561, 404, 718, 982 is 1.
Step 1: Since 561 > 404, we apply the division lemma to 561 and 404, to get
561 = 404 x 1 + 157
Step 2: Since the reminder 404 ≠ 0, we apply division lemma to 157 and 404, to get
404 = 157 x 2 + 90
Step 3: We consider the new divisor 157 and the new remainder 90, and apply the division lemma to get
157 = 90 x 1 + 67
We consider the new divisor 90 and the new remainder 67,and apply the division lemma to get
90 = 67 x 1 + 23
We consider the new divisor 67 and the new remainder 23,and apply the division lemma to get
67 = 23 x 2 + 21
We consider the new divisor 23 and the new remainder 21,and apply the division lemma to get
23 = 21 x 1 + 2
We consider the new divisor 21 and the new remainder 2,and apply the division lemma to get
21 = 2 x 10 + 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 404 is 1
Notice that 1 = HCF(2,1) = HCF(21,2) = HCF(23,21) = HCF(67,23) = HCF(90,67) = HCF(157,90) = HCF(404,157) = HCF(561,404) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 718 > 1, we apply the division lemma to 718 and 1, to get
718 = 1 x 718 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 718 is 1
Notice that 1 = HCF(718,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 982 > 1, we apply the division lemma to 982 and 1, to get
982 = 1 x 982 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 982 is 1
Notice that 1 = HCF(982,1) .
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, 404, 718, 982?
Answer: HCF of 561, 404, 718, 982 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 561, 404, 718, 982 using Euclid's Algorithm?
Answer: For arbitrary numbers 561, 404, 718, 982 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.