Highest Common Factor of 357, 584 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 357, 584 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 357, 584 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 357, 584 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 357, 584 is 1.

HCF(357, 584) = 1

HCF of 357, 584 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

HCF of:

Highest common factor (HCF) of 357, 584 is 1.

Highest Common Factor of 357,584 using Euclid's algorithm

Highest Common Factor of 357,584 is 1

Step 1: Since 584 > 357, we apply the division lemma to 584 and 357, to get

584 = 357 x 1 + 227

Step 2: Since the reminder 357 ≠ 0, we apply division lemma to 227 and 357, to get

357 = 227 x 1 + 130

Step 3: We consider the new divisor 227 and the new remainder 130, and apply the division lemma to get

227 = 130 x 1 + 97

We consider the new divisor 130 and the new remainder 97,and apply the division lemma to get

130 = 97 x 1 + 33

We consider the new divisor 97 and the new remainder 33,and apply the division lemma to get

97 = 33 x 2 + 31

We consider the new divisor 33 and the new remainder 31,and apply the division lemma to get

33 = 31 x 1 + 2

We consider the new divisor 31 and the new remainder 2,and apply the division lemma to get

31 = 2 x 15 + 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 357 and 584 is 1

Notice that 1 = HCF(2,1) = HCF(31,2) = HCF(33,31) = HCF(97,33) = HCF(130,97) = HCF(227,130) = HCF(357,227) = HCF(584,357) .

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Frequently Asked Questions on HCF of 357, 584 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 357, 584?

Answer: HCF of 357, 584 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 357, 584 using Euclid's Algorithm?

Answer: For arbitrary numbers 357, 584 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.