Highest Common Factor of 473, 352, 660 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 473, 352, 660 i.e. 11 the largest integer that leaves a remainder zero for all numbers.
HCF of 473, 352, 660 is 11 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 473, 352, 660 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 473, 352, 660 is 11.
HCF(473, 352, 660) = 11
HCF of 473, 352, 660 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 473, 352, 660 is 11.
Highest Common Factor of 473,352,660 is 11
Step 1: Since 473 > 352, we apply the division lemma to 473 and 352, to get
473 = 352 x 1 + 121
Step 2: Since the reminder 352 ≠ 0, we apply division lemma to 121 and 352, to get
352 = 121 x 2 + 110
Step 3: We consider the new divisor 121 and the new remainder 110, and apply the division lemma to get
121 = 110 x 1 + 11
We consider the new divisor 110 and the new remainder 11, and apply the division lemma to get
110 = 11 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 11, the HCF of 473 and 352 is 11
Notice that 11 = HCF(110,11) = HCF(121,110) = HCF(352,121) = HCF(473,352) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 660 > 11, we apply the division lemma to 660 and 11, to get
660 = 11 x 60 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 11, the HCF of 11 and 660 is 11
Notice that 11 = HCF(660,11) .
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Frequently Asked Questions on HCF of 473, 352, 660 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 473, 352, 660?
Answer: HCF of 473, 352, 660 is 11 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 473, 352, 660 using Euclid's Algorithm?
Answer: For arbitrary numbers 473, 352, 660 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
