Highest Common Factor of 285, 430, 460 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 285, 430, 460 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 285, 430, 460 is 5 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 285, 430, 460 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 285, 430, 460 is 5.
HCF(285, 430, 460) = 5
HCF of 285, 430, 460 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 285, 430, 460 is 5.
Highest Common Factor of 285,430,460 is 5
Step 1: Since 430 > 285, we apply the division lemma to 430 and 285, to get
430 = 285 x 1 + 145
Step 2: Since the reminder 285 ≠ 0, we apply division lemma to 145 and 285, to get
285 = 145 x 1 + 140
Step 3: We consider the new divisor 145 and the new remainder 140, and apply the division lemma to get
145 = 140 x 1 + 5
We consider the new divisor 140 and the new remainder 5, and apply the division lemma to get
140 = 5 x 28 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 285 and 430 is 5
Notice that 5 = HCF(140,5) = HCF(145,140) = HCF(285,145) = HCF(430,285) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 460 > 5, we apply the division lemma to 460 and 5, to get
460 = 5 x 92 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 5 and 460 is 5
Notice that 5 = HCF(460,5) .
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Frequently Asked Questions on HCF of 285, 430, 460 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 285, 430, 460?
Answer: HCF of 285, 430, 460 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 285, 430, 460 using Euclid's Algorithm?
Answer: For arbitrary numbers 285, 430, 460 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.