Highest Common Factor of 578, 360, 888 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 578, 360, 888 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 578, 360, 888 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 578, 360, 888 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 578, 360, 888 is 2.
HCF(578, 360, 888) = 2
HCF of 578, 360, 888 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 578, 360, 888 is 2.
Highest Common Factor of 578,360,888 is 2
Step 1: Since 578 > 360, we apply the division lemma to 578 and 360, to get
578 = 360 x 1 + 218
Step 2: Since the reminder 360 ≠ 0, we apply division lemma to 218 and 360, to get
360 = 218 x 1 + 142
Step 3: We consider the new divisor 218 and the new remainder 142, and apply the division lemma to get
218 = 142 x 1 + 76
We consider the new divisor 142 and the new remainder 76,and apply the division lemma to get
142 = 76 x 1 + 66
We consider the new divisor 76 and the new remainder 66,and apply the division lemma to get
76 = 66 x 1 + 10
We consider the new divisor 66 and the new remainder 10,and apply the division lemma to get
66 = 10 x 6 + 6
We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get
10 = 6 x 1 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 578 and 360 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(66,10) = HCF(76,66) = HCF(142,76) = HCF(218,142) = HCF(360,218) = HCF(578,360) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 888 > 2, we apply the division lemma to 888 and 2, to get
888 = 2 x 444 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 888 is 2
Notice that 2 = HCF(888,2) .
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Frequently Asked Questions on HCF of 578, 360, 888 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 578, 360, 888?
Answer: HCF of 578, 360, 888 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 578, 360, 888 using Euclid's Algorithm?
Answer: For arbitrary numbers 578, 360, 888 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
