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 567, 982, 82 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 567, 982, 82 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 567, 982, 82 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 567, 982, 82 is 1.
HCF(567, 982, 82) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 567, 982, 82 is 1.
Step 1: Since 982 > 567, we apply the division lemma to 982 and 567, to get
982 = 567 x 1 + 415
Step 2: Since the reminder 567 ≠ 0, we apply division lemma to 415 and 567, to get
567 = 415 x 1 + 152
Step 3: We consider the new divisor 415 and the new remainder 152, and apply the division lemma to get
415 = 152 x 2 + 111
We consider the new divisor 152 and the new remainder 111,and apply the division lemma to get
152 = 111 x 1 + 41
We consider the new divisor 111 and the new remainder 41,and apply the division lemma to get
111 = 41 x 2 + 29
We consider the new divisor 41 and the new remainder 29,and apply the division lemma to get
41 = 29 x 1 + 12
We consider the new divisor 29 and the new remainder 12,and apply the division lemma to get
29 = 12 x 2 + 5
We consider the new divisor 12 and the new remainder 5,and apply the division lemma to get
12 = 5 x 2 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 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 567 and 982 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(12,5) = HCF(29,12) = HCF(41,29) = HCF(111,41) = HCF(152,111) = HCF(415,152) = HCF(567,415) = HCF(982,567) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 82 > 1, we apply the division lemma to 82 and 1, to get
82 = 1 x 82 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 82 is 1
Notice that 1 = HCF(82,1) .
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 567, 982, 82?
Answer: HCF of 567, 982, 82 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 567, 982, 82 using Euclid's Algorithm?
Answer: For arbitrary numbers 567, 982, 82 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.