Highest Common Factor of 768, 432, 693 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 768, 432, 693 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 768, 432, 693 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 768, 432, 693 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 768, 432, 693 is 3.
HCF(768, 432, 693) = 3
HCF of 768, 432, 693 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 768, 432, 693 is 3.
Highest Common Factor of 768,432,693 is 3
Step 1: Since 768 > 432, we apply the division lemma to 768 and 432, to get
768 = 432 x 1 + 336
Step 2: Since the reminder 432 ≠ 0, we apply division lemma to 336 and 432, to get
432 = 336 x 1 + 96
Step 3: We consider the new divisor 336 and the new remainder 96, and apply the division lemma to get
336 = 96 x 3 + 48
We consider the new divisor 96 and the new remainder 48, and apply the division lemma to get
96 = 48 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 48, the HCF of 768 and 432 is 48
Notice that 48 = HCF(96,48) = HCF(336,96) = HCF(432,336) = HCF(768,432) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 693 > 48, we apply the division lemma to 693 and 48, to get
693 = 48 x 14 + 21
Step 2: Since the reminder 48 ≠ 0, we apply division lemma to 21 and 48, to get
48 = 21 x 2 + 6
Step 3: We consider the new divisor 21 and the new remainder 6, and apply the division lemma to get
21 = 6 x 3 + 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 48 and 693 is 3
Notice that 3 = HCF(6,3) = HCF(21,6) = HCF(48,21) = HCF(693,48) .
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Frequently Asked Questions on HCF of 768, 432, 693 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 768, 432, 693?
Answer: HCF of 768, 432, 693 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 768, 432, 693 using Euclid's Algorithm?
Answer: For arbitrary numbers 768, 432, 693 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.