Highest Common Factor of 378, 576, 693, 320 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 378, 576, 693, 320 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 378, 576, 693, 320 is 1 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 378, 576, 693, 320 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 378, 576, 693, 320 is 1.
HCF(378, 576, 693, 320) = 1
HCF of 378, 576, 693, 320 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 378, 576, 693, 320 is 1.
Highest Common Factor of 378,576,693,320 is 1
Step 1: Since 576 > 378, we apply the division lemma to 576 and 378, to get
576 = 378 x 1 + 198
Step 2: Since the reminder 378 ≠ 0, we apply division lemma to 198 and 378, to get
378 = 198 x 1 + 180
Step 3: We consider the new divisor 198 and the new remainder 180, and apply the division lemma to get
198 = 180 x 1 + 18
We consider the new divisor 180 and the new remainder 18, and apply the division lemma to get
180 = 18 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 18, the HCF of 378 and 576 is 18
Notice that 18 = HCF(180,18) = HCF(198,180) = HCF(378,198) = HCF(576,378) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 693 > 18, we apply the division lemma to 693 and 18, to get
693 = 18 x 38 + 9
Step 2: Since the reminder 18 ≠ 0, we apply division lemma to 9 and 18, to get
18 = 9 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 18 and 693 is 9
Notice that 9 = HCF(18,9) = HCF(693,18) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 320 > 9, we apply the division lemma to 320 and 9, to get
320 = 9 x 35 + 5
Step 2: Since the reminder 9 ≠ 0, we apply division lemma to 5 and 9, to get
9 = 5 x 1 + 4
Step 3: We consider the new divisor 5 and the new remainder 4, and apply the division lemma to get
5 = 4 x 1 + 1
We consider the new divisor 4 and the new remainder 1, and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 9 and 320 is 1
Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(320,9) .
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Frequently Asked Questions on HCF of 378, 576, 693, 320 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 378, 576, 693, 320?
Answer: HCF of 378, 576, 693, 320 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 378, 576, 693, 320 using Euclid's Algorithm?
Answer: For arbitrary numbers 378, 576, 693, 320 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.