Highest Common Factor of 666, 849, 17, 979 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 666, 849, 17, 979 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 666, 849, 17, 979 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 666, 849, 17, 979 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 666, 849, 17, 979 is 1.
HCF(666, 849, 17, 979) = 1
HCF of 666, 849, 17, 979 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 666, 849, 17, 979 is 1.
Highest Common Factor of 666,849,17,979 is 1
Step 1: Since 849 > 666, we apply the division lemma to 849 and 666, to get
849 = 666 x 1 + 183
Step 2: Since the reminder 666 ≠ 0, we apply division lemma to 183 and 666, to get
666 = 183 x 3 + 117
Step 3: We consider the new divisor 183 and the new remainder 117, and apply the division lemma to get
183 = 117 x 1 + 66
We consider the new divisor 117 and the new remainder 66,and apply the division lemma to get
117 = 66 x 1 + 51
We consider the new divisor 66 and the new remainder 51,and apply the division lemma to get
66 = 51 x 1 + 15
We consider the new divisor 51 and the new remainder 15,and apply the division lemma to get
51 = 15 x 3 + 6
We consider the new divisor 15 and the new remainder 6,and apply the division lemma to get
15 = 6 x 2 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 666 and 849 is 3
Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(51,15) = HCF(66,51) = HCF(117,66) = HCF(183,117) = HCF(666,183) = HCF(849,666) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 17 > 3, we apply the division lemma to 17 and 3, to get
17 = 3 x 5 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: 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 3 and 17 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(17,3) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 979 > 1, we apply the division lemma to 979 and 1, to get
979 = 1 x 979 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 979 is 1
Notice that 1 = HCF(979,1) .
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Frequently Asked Questions on HCF of 666, 849, 17, 979 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 666, 849, 17, 979?
Answer: HCF of 666, 849, 17, 979 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 666, 849, 17, 979 using Euclid's Algorithm?
Answer: For arbitrary numbers 666, 849, 17, 979 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.