Highest Common Factor of 552, 9730, 9867 using Euclid's algorithm
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 552, 9730, 9867 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 552, 9730, 9867 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 552, 9730, 9867 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 552, 9730, 9867 is 1.
HCF(552, 9730, 9867) = 1
HCF of 552, 9730, 9867 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 552, 9730, 9867 is 1.
Highest Common Factor of 552,9730,9867 is 1
Step 1: Since 9730 > 552, we apply the division lemma to 9730 and 552, to get
9730 = 552 x 17 + 346
Step 2: Since the reminder 552 ≠ 0, we apply division lemma to 346 and 552, to get
552 = 346 x 1 + 206
Step 3: We consider the new divisor 346 and the new remainder 206, and apply the division lemma to get
346 = 206 x 1 + 140
We consider the new divisor 206 and the new remainder 140,and apply the division lemma to get
206 = 140 x 1 + 66
We consider the new divisor 140 and the new remainder 66,and apply the division lemma to get
140 = 66 x 2 + 8
We consider the new divisor 66 and the new remainder 8,and apply the division lemma to get
66 = 8 x 8 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 552 and 9730 is 2
Notice that 2 = HCF(8,2) = HCF(66,8) = HCF(140,66) = HCF(206,140) = HCF(346,206) = HCF(552,346) = HCF(9730,552) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 9867 > 2, we apply the division lemma to 9867 and 2, to get
9867 = 2 x 4933 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 9867 is 1
Notice that 1 = HCF(2,1) = HCF(9867,2) .
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Frequently Asked Questions on HCF of 552, 9730, 9867 using Euclid's Algorithm
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 552, 9730, 9867?
Answer: HCF of 552, 9730, 9867 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 552, 9730, 9867 using Euclid's Algorithm?
Answer: For arbitrary numbers 552, 9730, 9867 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.