Highest Common Factor of 732, 305, 471, 530 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 732, 305, 471, 530 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 732, 305, 471, 530 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 732, 305, 471, 530 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 732, 305, 471, 530 is 1.
HCF(732, 305, 471, 530) = 1
HCF of 732, 305, 471, 530 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 732, 305, 471, 530 is 1.
Highest Common Factor of 732,305,471,530 is 1
Step 1: Since 732 > 305, we apply the division lemma to 732 and 305, to get
732 = 305 x 2 + 122
Step 2: Since the reminder 305 ≠ 0, we apply division lemma to 122 and 305, to get
305 = 122 x 2 + 61
Step 3: We consider the new divisor 122 and the new remainder 61, and apply the division lemma to get
122 = 61 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 61, the HCF of 732 and 305 is 61
Notice that 61 = HCF(122,61) = HCF(305,122) = HCF(732,305) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 471 > 61, we apply the division lemma to 471 and 61, to get
471 = 61 x 7 + 44
Step 2: Since the reminder 61 ≠ 0, we apply division lemma to 44 and 61, to get
61 = 44 x 1 + 17
Step 3: We consider the new divisor 44 and the new remainder 17, and apply the division lemma to get
44 = 17 x 2 + 10
We consider the new divisor 17 and the new remainder 10,and apply the division lemma to get
17 = 10 x 1 + 7
We consider the new divisor 10 and the new remainder 7,and apply the division lemma to get
10 = 7 x 1 + 3
We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get
7 = 3 x 2 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 61 and 471 is 1
Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(10,7) = HCF(17,10) = HCF(44,17) = HCF(61,44) = HCF(471,61) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 530 > 1, we apply the division lemma to 530 and 1, to get
530 = 1 x 530 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 530 is 1
Notice that 1 = HCF(530,1) .
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Frequently Asked Questions on HCF of 732, 305, 471, 530 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 732, 305, 471, 530?
Answer: HCF of 732, 305, 471, 530 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 732, 305, 471, 530 using Euclid's Algorithm?
Answer: For arbitrary numbers 732, 305, 471, 530 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.