Highest Common Factor of 960, 676, 680 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, 676, 680 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 960, 676, 680 is 4 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, 676, 680 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, 676, 680 is 4.
HCF(960, 676, 680) = 4
HCF of 960, 676, 680 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, 676, 680 is 4.
Highest Common Factor of 960,676,680 is 4
Step 1: Since 960 > 676, we apply the division lemma to 960 and 676, to get
960 = 676 x 1 + 284
Step 2: Since the reminder 676 ≠ 0, we apply division lemma to 284 and 676, to get
676 = 284 x 2 + 108
Step 3: We consider the new divisor 284 and the new remainder 108, and apply the division lemma to get
284 = 108 x 2 + 68
We consider the new divisor 108 and the new remainder 68,and apply the division lemma to get
108 = 68 x 1 + 40
We consider the new divisor 68 and the new remainder 40,and apply the division lemma to get
68 = 40 x 1 + 28
We consider the new divisor 40 and the new remainder 28,and apply the division lemma to get
40 = 28 x 1 + 12
We consider the new divisor 28 and the new remainder 12,and apply the division lemma to get
28 = 12 x 2 + 4
We consider the new divisor 12 and the new remainder 4,and apply the division lemma to get
12 = 4 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 960 and 676 is 4
Notice that 4 = HCF(12,4) = HCF(28,12) = HCF(40,28) = HCF(68,40) = HCF(108,68) = HCF(284,108) = HCF(676,284) = HCF(960,676) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 680 > 4, we apply the division lemma to 680 and 4, to get
680 = 4 x 170 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 4 and 680 is 4
Notice that 4 = HCF(680,4) .
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Frequently Asked Questions on HCF of 960, 676, 680 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, 676, 680?
Answer: HCF of 960, 676, 680 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 960, 676, 680 using Euclid's Algorithm?
Answer: For arbitrary numbers 960, 676, 680 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.