Highest Common Factor of 377, 578, 254 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 377, 578, 254 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 377, 578, 254 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 377, 578, 254 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 377, 578, 254 is 1.
HCF(377, 578, 254) = 1
HCF of 377, 578, 254 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 377, 578, 254 is 1.
Highest Common Factor of 377,578,254 is 1
Step 1: Since 578 > 377, we apply the division lemma to 578 and 377, to get
578 = 377 x 1 + 201
Step 2: Since the reminder 377 ≠ 0, we apply division lemma to 201 and 377, to get
377 = 201 x 1 + 176
Step 3: We consider the new divisor 201 and the new remainder 176, and apply the division lemma to get
201 = 176 x 1 + 25
We consider the new divisor 176 and the new remainder 25,and apply the division lemma to get
176 = 25 x 7 + 1
We consider the new divisor 25 and the new remainder 1,and apply the division lemma to get
25 = 1 x 25 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 377 and 578 is 1
Notice that 1 = HCF(25,1) = HCF(176,25) = HCF(201,176) = HCF(377,201) = HCF(578,377) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 254 > 1, we apply the division lemma to 254 and 1, to get
254 = 1 x 254 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 254 is 1
Notice that 1 = HCF(254,1) .
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Frequently Asked Questions on HCF of 377, 578, 254 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 377, 578, 254?
Answer: HCF of 377, 578, 254 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 377, 578, 254 using Euclid's Algorithm?
Answer: For arbitrary numbers 377, 578, 254 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.