Highest Common Factor of 565, 452, 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 565, 452, 460 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 565, 452, 460 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 565, 452, 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 565, 452, 460 is 1.
HCF(565, 452, 460) = 1
HCF of 565, 452, 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 565, 452, 460 is 1.
Highest Common Factor of 565,452,460 is 1
Step 1: Since 565 > 452, we apply the division lemma to 565 and 452, to get
565 = 452 x 1 + 113
Step 2: Since the reminder 452 ≠ 0, we apply division lemma to 113 and 452, to get
452 = 113 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 113, the HCF of 565 and 452 is 113
Notice that 113 = HCF(452,113) = HCF(565,452) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 460 > 113, we apply the division lemma to 460 and 113, to get
460 = 113 x 4 + 8
Step 2: Since the reminder 113 ≠ 0, we apply division lemma to 8 and 113, to get
113 = 8 x 14 + 1
Step 3: We consider the new divisor 8 and the new remainder 1, and apply the division lemma to get
8 = 1 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 113 and 460 is 1
Notice that 1 = HCF(8,1) = HCF(113,8) = HCF(460,113) .
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Frequently Asked Questions on HCF of 565, 452, 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 565, 452, 460?
Answer: HCF of 565, 452, 460 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 565, 452, 460 using Euclid's Algorithm?
Answer: For arbitrary numbers 565, 452, 460 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.