Highest Common Factor of 574, 357, 341 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 574, 357, 341 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 574, 357, 341 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 574, 357, 341 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 574, 357, 341 is 1.
HCF(574, 357, 341) = 1
HCF of 574, 357, 341 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 574, 357, 341 is 1.
Highest Common Factor of 574,357,341 is 1
Step 1: Since 574 > 357, we apply the division lemma to 574 and 357, to get
574 = 357 x 1 + 217
Step 2: Since the reminder 357 ≠ 0, we apply division lemma to 217 and 357, to get
357 = 217 x 1 + 140
Step 3: We consider the new divisor 217 and the new remainder 140, and apply the division lemma to get
217 = 140 x 1 + 77
We consider the new divisor 140 and the new remainder 77,and apply the division lemma to get
140 = 77 x 1 + 63
We consider the new divisor 77 and the new remainder 63,and apply the division lemma to get
77 = 63 x 1 + 14
We consider the new divisor 63 and the new remainder 14,and apply the division lemma to get
63 = 14 x 4 + 7
We consider the new divisor 14 and the new remainder 7,and apply the division lemma to get
14 = 7 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 574 and 357 is 7
Notice that 7 = HCF(14,7) = HCF(63,14) = HCF(77,63) = HCF(140,77) = HCF(217,140) = HCF(357,217) = HCF(574,357) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 341 > 7, we apply the division lemma to 341 and 7, to get
341 = 7 x 48 + 5
Step 2: Since the reminder 7 ≠ 0, we apply division lemma to 5 and 7, to get
7 = 5 x 1 + 2
Step 3: We consider the new divisor 5 and the new remainder 2, and apply the division lemma to get
5 = 2 x 2 + 1
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 7 and 341 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(341,7) .
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Frequently Asked Questions on HCF of 574, 357, 341 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 574, 357, 341?
Answer: HCF of 574, 357, 341 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 574, 357, 341 using Euclid's Algorithm?
Answer: For arbitrary numbers 574, 357, 341 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.