Highest Common Factor of 440, 176, 578 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 440, 176, 578 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 440, 176, 578 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 440, 176, 578 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 440, 176, 578 is 2.
HCF(440, 176, 578) = 2
HCF of 440, 176, 578 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 440, 176, 578 is 2.
Highest Common Factor of 440,176,578 is 2
Step 1: Since 440 > 176, we apply the division lemma to 440 and 176, to get
440 = 176 x 2 + 88
Step 2: Since the reminder 176 ≠ 0, we apply division lemma to 88 and 176, to get
176 = 88 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 88, the HCF of 440 and 176 is 88
Notice that 88 = HCF(176,88) = HCF(440,176) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 578 > 88, we apply the division lemma to 578 and 88, to get
578 = 88 x 6 + 50
Step 2: Since the reminder 88 ≠ 0, we apply division lemma to 50 and 88, to get
88 = 50 x 1 + 38
Step 3: We consider the new divisor 50 and the new remainder 38, and apply the division lemma to get
50 = 38 x 1 + 12
We consider the new divisor 38 and the new remainder 12,and apply the division lemma to get
38 = 12 x 3 + 2
We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get
12 = 2 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 88 and 578 is 2
Notice that 2 = HCF(12,2) = HCF(38,12) = HCF(50,38) = HCF(88,50) = HCF(578,88) .
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Frequently Asked Questions on HCF of 440, 176, 578 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 440, 176, 578?
Answer: HCF of 440, 176, 578 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 440, 176, 578 using Euclid's Algorithm?
Answer: For arbitrary numbers 440, 176, 578 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.