Highest Common Factor of 364, 584, 715 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 364, 584, 715 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 364, 584, 715 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 364, 584, 715 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 364, 584, 715 is 1.

HCF(364, 584, 715) = 1

HCF of 364, 584, 715 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 364, 584, 715 is 1.

Highest Common Factor of 364,584,715 using Euclid's algorithm

Highest Common Factor of 364,584,715 is 1

Step 1: Since 584 > 364, we apply the division lemma to 584 and 364, to get

584 = 364 x 1 + 220

Step 2: Since the reminder 364 ≠ 0, we apply division lemma to 220 and 364, to get

364 = 220 x 1 + 144

Step 3: We consider the new divisor 220 and the new remainder 144, and apply the division lemma to get

220 = 144 x 1 + 76

We consider the new divisor 144 and the new remainder 76,and apply the division lemma to get

144 = 76 x 1 + 68

We consider the new divisor 76 and the new remainder 68,and apply the division lemma to get

76 = 68 x 1 + 8

We consider the new divisor 68 and the new remainder 8,and apply the division lemma to get

68 = 8 x 8 + 4

We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get

8 = 4 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 364 and 584 is 4

Notice that 4 = HCF(8,4) = HCF(68,8) = HCF(76,68) = HCF(144,76) = HCF(220,144) = HCF(364,220) = HCF(584,364) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 715 > 4, we apply the division lemma to 715 and 4, to get

715 = 4 x 178 + 3

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 3 and 4, to get

4 = 3 x 1 + 1

Step 3: We consider the new divisor 3 and the new remainder 1, and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4 and 715 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(715,4) .

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Frequently Asked Questions on HCF of 364, 584, 715 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 364, 584, 715?

Answer: HCF of 364, 584, 715 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 364, 584, 715 using Euclid's Algorithm?

Answer: For arbitrary numbers 364, 584, 715 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.