Highest Common Factor of 576, 960, 33 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 576, 960, 33 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 576, 960, 33 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 576, 960, 33 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 576, 960, 33 is 3.
HCF(576, 960, 33) = 3
HCF of 576, 960, 33 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 576, 960, 33 is 3.
Highest Common Factor of 576,960,33 is 3
Step 1: Since 960 > 576, we apply the division lemma to 960 and 576, to get
960 = 576 x 1 + 384
Step 2: Since the reminder 576 ≠ 0, we apply division lemma to 384 and 576, to get
576 = 384 x 1 + 192
Step 3: We consider the new divisor 384 and the new remainder 192, and apply the division lemma to get
384 = 192 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 192, the HCF of 576 and 960 is 192
Notice that 192 = HCF(384,192) = HCF(576,384) = HCF(960,576) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 192 > 33, we apply the division lemma to 192 and 33, to get
192 = 33 x 5 + 27
Step 2: Since the reminder 33 ≠ 0, we apply division lemma to 27 and 33, to get
33 = 27 x 1 + 6
Step 3: We consider the new divisor 27 and the new remainder 6, and apply the division lemma to get
27 = 6 x 4 + 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 192 and 33 is 3
Notice that 3 = HCF(6,3) = HCF(27,6) = HCF(33,27) = HCF(192,33) .
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Frequently Asked Questions on HCF of 576, 960, 33 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 576, 960, 33?
Answer: HCF of 576, 960, 33 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 576, 960, 33 using Euclid's Algorithm?
Answer: For arbitrary numbers 576, 960, 33 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.