Highest Common Factor of 660, 792, 166 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 660, 792, 166 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 660, 792, 166 is 2 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 660, 792, 166 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 660, 792, 166 is 2.
HCF(660, 792, 166) = 2
HCF of 660, 792, 166 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 660, 792, 166 is 2.
Highest Common Factor of 660,792,166 is 2
Step 1: Since 792 > 660, we apply the division lemma to 792 and 660, to get
792 = 660 x 1 + 132
Step 2: Since the reminder 660 ≠ 0, we apply division lemma to 132 and 660, to get
660 = 132 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 132, the HCF of 660 and 792 is 132
Notice that 132 = HCF(660,132) = HCF(792,660) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 166 > 132, we apply the division lemma to 166 and 132, to get
166 = 132 x 1 + 34
Step 2: Since the reminder 132 ≠ 0, we apply division lemma to 34 and 132, to get
132 = 34 x 3 + 30
Step 3: We consider the new divisor 34 and the new remainder 30, and apply the division lemma to get
34 = 30 x 1 + 4
We consider the new divisor 30 and the new remainder 4,and apply the division lemma to get
30 = 4 x 7 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 132 and 166 is 2
Notice that 2 = HCF(4,2) = HCF(30,4) = HCF(34,30) = HCF(132,34) = HCF(166,132) .
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Frequently Asked Questions on HCF of 660, 792, 166 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 660, 792, 166?
Answer: HCF of 660, 792, 166 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 660, 792, 166 using Euclid's Algorithm?
Answer: For arbitrary numbers 660, 792, 166 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.