Highest Common Factor of 372, 589, 688 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 372, 589, 688 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 372, 589, 688 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 372, 589, 688 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 372, 589, 688 is 1.

HCF(372, 589, 688) = 1

HCF of 372, 589, 688 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 372, 589, 688 is 1.

Highest Common Factor of 372,589,688 using Euclid's algorithm

Highest Common Factor of 372,589,688 is 1

Step 1: Since 589 > 372, we apply the division lemma to 589 and 372, to get

589 = 372 x 1 + 217

Step 2: Since the reminder 372 ≠ 0, we apply division lemma to 217 and 372, to get

372 = 217 x 1 + 155

Step 3: We consider the new divisor 217 and the new remainder 155, and apply the division lemma to get

217 = 155 x 1 + 62

We consider the new divisor 155 and the new remainder 62,and apply the division lemma to get

155 = 62 x 2 + 31

We consider the new divisor 62 and the new remainder 31,and apply the division lemma to get

62 = 31 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 31, the HCF of 372 and 589 is 31

Notice that 31 = HCF(62,31) = HCF(155,62) = HCF(217,155) = HCF(372,217) = HCF(589,372) .

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

Step 1: Since 688 > 31, we apply the division lemma to 688 and 31, to get

688 = 31 x 22 + 6

Step 2: Since the reminder 31 ≠ 0, we apply division lemma to 6 and 31, to get

31 = 6 x 5 + 1

Step 3: We consider the new divisor 6 and the new remainder 1, and apply the division lemma to get

6 = 1 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 31 and 688 is 1

Notice that 1 = HCF(6,1) = HCF(31,6) = HCF(688,31) .

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Frequently Asked Questions on HCF of 372, 589, 688 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 372, 589, 688?

Answer: HCF of 372, 589, 688 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 372, 589, 688 using Euclid's Algorithm?

Answer: For arbitrary numbers 372, 589, 688 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.