Highest Common Factor of 472, 352, 576 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 472, 352, 576 i.e. 8 the largest integer that leaves a remainder zero for all numbers.
HCF of 472, 352, 576 is 8 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 472, 352, 576 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 472, 352, 576 is 8.
HCF(472, 352, 576) = 8
HCF of 472, 352, 576 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 472, 352, 576 is 8.
Highest Common Factor of 472,352,576 is 8
Step 1: Since 472 > 352, we apply the division lemma to 472 and 352, to get
472 = 352 x 1 + 120
Step 2: Since the reminder 352 ≠ 0, we apply division lemma to 120 and 352, to get
352 = 120 x 2 + 112
Step 3: We consider the new divisor 120 and the new remainder 112, and apply the division lemma to get
120 = 112 x 1 + 8
We consider the new divisor 112 and the new remainder 8, and apply the division lemma to get
112 = 8 x 14 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 472 and 352 is 8
Notice that 8 = HCF(112,8) = HCF(120,112) = HCF(352,120) = HCF(472,352) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 576 > 8, we apply the division lemma to 576 and 8, to get
576 = 8 x 72 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 8 and 576 is 8
Notice that 8 = HCF(576,8) .
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Frequently Asked Questions on HCF of 472, 352, 576 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 472, 352, 576?
Answer: HCF of 472, 352, 576 is 8 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 472, 352, 576 using Euclid's Algorithm?
Answer: For arbitrary numbers 472, 352, 576 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.