Highest Common Factor of 356, 578, 131 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 356, 578, 131 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 356, 578, 131 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 356, 578, 131 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 356, 578, 131 is 1.
HCF(356, 578, 131) = 1
HCF of 356, 578, 131 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 356, 578, 131 is 1.
Highest Common Factor of 356,578,131 is 1
Step 1: Since 578 > 356, we apply the division lemma to 578 and 356, to get
578 = 356 x 1 + 222
Step 2: Since the reminder 356 ≠ 0, we apply division lemma to 222 and 356, to get
356 = 222 x 1 + 134
Step 3: We consider the new divisor 222 and the new remainder 134, and apply the division lemma to get
222 = 134 x 1 + 88
We consider the new divisor 134 and the new remainder 88,and apply the division lemma to get
134 = 88 x 1 + 46
We consider the new divisor 88 and the new remainder 46,and apply the division lemma to get
88 = 46 x 1 + 42
We consider the new divisor 46 and the new remainder 42,and apply the division lemma to get
46 = 42 x 1 + 4
We consider the new divisor 42 and the new remainder 4,and apply the division lemma to get
42 = 4 x 10 + 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 356 and 578 is 2
Notice that 2 = HCF(4,2) = HCF(42,4) = HCF(46,42) = HCF(88,46) = HCF(134,88) = HCF(222,134) = HCF(356,222) = HCF(578,356) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 131 > 2, we apply the division lemma to 131 and 2, to get
131 = 2 x 65 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 131 is 1
Notice that 1 = HCF(2,1) = HCF(131,2) .
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Frequently Asked Questions on HCF of 356, 578, 131 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 356, 578, 131?
Answer: HCF of 356, 578, 131 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 356, 578, 131 using Euclid's Algorithm?
Answer: For arbitrary numbers 356, 578, 131 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.