Highest Common Factor of 960, 672, 393 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, 672, 393 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 960, 672, 393 is 3 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, 672, 393 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, 672, 393 is 3.
HCF(960, 672, 393) = 3
HCF of 960, 672, 393 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, 672, 393 is 3.
Highest Common Factor of 960,672,393 is 3
Step 1: Since 960 > 672, we apply the division lemma to 960 and 672, to get
960 = 672 x 1 + 288
Step 2: Since the reminder 672 ≠ 0, we apply division lemma to 288 and 672, to get
672 = 288 x 2 + 96
Step 3: We consider the new divisor 288 and the new remainder 96, and apply the division lemma to get
288 = 96 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 96, the HCF of 960 and 672 is 96
Notice that 96 = HCF(288,96) = HCF(672,288) = HCF(960,672) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 393 > 96, we apply the division lemma to 393 and 96, to get
393 = 96 x 4 + 9
Step 2: Since the reminder 96 ≠ 0, we apply division lemma to 9 and 96, to get
96 = 9 x 10 + 6
Step 3: We consider the new divisor 9 and the new remainder 6, and apply the division lemma to get
9 = 6 x 1 + 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 96 and 393 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(96,9) = HCF(393,96) .
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Frequently Asked Questions on HCF of 960, 672, 393 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, 672, 393?
Answer: HCF of 960, 672, 393 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 960, 672, 393 using Euclid's Algorithm?
Answer: For arbitrary numbers 960, 672, 393 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.