Highest Common Factor of 960, 680, 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 960, 680, 166 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 960, 680, 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 960, 680, 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 960, 680, 166 is 2.
HCF(960, 680, 166) = 2
HCF of 960, 680, 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 960, 680, 166 is 2.
Highest Common Factor of 960,680,166 is 2
Step 1: Since 960 > 680, we apply the division lemma to 960 and 680, to get
960 = 680 x 1 + 280
Step 2: Since the reminder 680 ≠ 0, we apply division lemma to 280 and 680, to get
680 = 280 x 2 + 120
Step 3: We consider the new divisor 280 and the new remainder 120, and apply the division lemma to get
280 = 120 x 2 + 40
We consider the new divisor 120 and the new remainder 40, and apply the division lemma to get
120 = 40 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 40, the HCF of 960 and 680 is 40
Notice that 40 = HCF(120,40) = HCF(280,120) = HCF(680,280) = HCF(960,680) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 166 > 40, we apply the division lemma to 166 and 40, to get
166 = 40 x 4 + 6
Step 2: Since the reminder 40 ≠ 0, we apply division lemma to 6 and 40, to get
40 = 6 x 6 + 4
Step 3: We consider the new divisor 6 and the new remainder 4, and apply the division lemma to get
6 = 4 x 1 + 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 40 and 166 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(40,6) = HCF(166,40) .
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Frequently Asked Questions on HCF of 960, 680, 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 960, 680, 166?
Answer: HCF of 960, 680, 166 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 960, 680, 166 using Euclid's Algorithm?
Answer: For arbitrary numbers 960, 680, 166 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.