Highest Common Factor of 885, 723, 560 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 885, 723, 560 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 885, 723, 560 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 885, 723, 560 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 885, 723, 560 is 1.
HCF(885, 723, 560) = 1
HCF of 885, 723, 560 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 885, 723, 560 is 1.
Highest Common Factor of 885,723,560 is 1
Step 1: Since 885 > 723, we apply the division lemma to 885 and 723, to get
885 = 723 x 1 + 162
Step 2: Since the reminder 723 ≠ 0, we apply division lemma to 162 and 723, to get
723 = 162 x 4 + 75
Step 3: We consider the new divisor 162 and the new remainder 75, and apply the division lemma to get
162 = 75 x 2 + 12
We consider the new divisor 75 and the new remainder 12,and apply the division lemma to get
75 = 12 x 6 + 3
We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 885 and 723 is 3
Notice that 3 = HCF(12,3) = HCF(75,12) = HCF(162,75) = HCF(723,162) = HCF(885,723) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 560 > 3, we apply the division lemma to 560 and 3, to get
560 = 3 x 186 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 560 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(560,3) .
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Frequently Asked Questions on HCF of 885, 723, 560 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 885, 723, 560?
Answer: HCF of 885, 723, 560 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 885, 723, 560 using Euclid's Algorithm?
Answer: For arbitrary numbers 885, 723, 560 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.