Highest Common Factor of 688, 375, 232, 606 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 688, 375, 232, 606 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 688, 375, 232, 606 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 688, 375, 232, 606 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 688, 375, 232, 606 is 1.

HCF(688, 375, 232, 606) = 1

HCF of 688, 375, 232, 606 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 688, 375, 232, 606 is 1.

Highest Common Factor of 688,375,232,606 using Euclid's algorithm

Highest Common Factor of 688,375,232,606 is 1

Step 1: Since 688 > 375, we apply the division lemma to 688 and 375, to get

688 = 375 x 1 + 313

Step 2: Since the reminder 375 ≠ 0, we apply division lemma to 313 and 375, to get

375 = 313 x 1 + 62

Step 3: We consider the new divisor 313 and the new remainder 62, and apply the division lemma to get

313 = 62 x 5 + 3

We consider the new divisor 62 and the new remainder 3,and apply the division lemma to get

62 = 3 x 20 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 688 and 375 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(62,3) = HCF(313,62) = HCF(375,313) = HCF(688,375) .

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

Step 1: Since 232 > 1, we apply the division lemma to 232 and 1, to get

232 = 1 x 232 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 232 is 1

Notice that 1 = HCF(232,1) .

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

Step 1: Since 606 > 1, we apply the division lemma to 606 and 1, to get

606 = 1 x 606 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 606 is 1

Notice that 1 = HCF(606,1) .

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Frequently Asked Questions on HCF of 688, 375, 232, 606 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 688, 375, 232, 606?

Answer: HCF of 688, 375, 232, 606 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 688, 375, 232, 606 using Euclid's Algorithm?

Answer: For arbitrary numbers 688, 375, 232, 606 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.