Highest Common Factor of 864, 560, 450 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 864, 560, 450 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 864, 560, 450 is 2 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 864, 560, 450 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 864, 560, 450 is 2.
HCF(864, 560, 450) = 2
HCF of 864, 560, 450 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 864, 560, 450 is 2.
Highest Common Factor of 864,560,450 is 2
Step 1: Since 864 > 560, we apply the division lemma to 864 and 560, to get
864 = 560 x 1 + 304
Step 2: Since the reminder 560 ≠ 0, we apply division lemma to 304 and 560, to get
560 = 304 x 1 + 256
Step 3: We consider the new divisor 304 and the new remainder 256, and apply the division lemma to get
304 = 256 x 1 + 48
We consider the new divisor 256 and the new remainder 48,and apply the division lemma to get
256 = 48 x 5 + 16
We consider the new divisor 48 and the new remainder 16,and apply the division lemma to get
48 = 16 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 16, the HCF of 864 and 560 is 16
Notice that 16 = HCF(48,16) = HCF(256,48) = HCF(304,256) = HCF(560,304) = HCF(864,560) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 450 > 16, we apply the division lemma to 450 and 16, to get
450 = 16 x 28 + 2
Step 2: Since the reminder 16 ≠ 0, we apply division lemma to 2 and 16, to get
16 = 2 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 16 and 450 is 2
Notice that 2 = HCF(16,2) = HCF(450,16) .
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Frequently Asked Questions on HCF of 864, 560, 450 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 864, 560, 450?
Answer: HCF of 864, 560, 450 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 864, 560, 450 using Euclid's Algorithm?
Answer: For arbitrary numbers 864, 560, 450 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.