Highest Common Factor of 705, 374, 645 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 705, 374, 645 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 705, 374, 645 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 705, 374, 645 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 705, 374, 645 is 1.

HCF(705, 374, 645) = 1

HCF of 705, 374, 645 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 705, 374, 645 is 1.

Highest Common Factor of 705,374,645 using Euclid's algorithm

Highest Common Factor of 705,374,645 is 1

Step 1: Since 705 > 374, we apply the division lemma to 705 and 374, to get

705 = 374 x 1 + 331

Step 2: Since the reminder 374 ≠ 0, we apply division lemma to 331 and 374, to get

374 = 331 x 1 + 43

Step 3: We consider the new divisor 331 and the new remainder 43, and apply the division lemma to get

331 = 43 x 7 + 30

We consider the new divisor 43 and the new remainder 30,and apply the division lemma to get

43 = 30 x 1 + 13

We consider the new divisor 30 and the new remainder 13,and apply the division lemma to get

30 = 13 x 2 + 4

We consider the new divisor 13 and the new remainder 4,and apply the division lemma to get

13 = 4 x 3 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 705 and 374 is 1

Notice that 1 = HCF(4,1) = HCF(13,4) = HCF(30,13) = HCF(43,30) = HCF(331,43) = HCF(374,331) = HCF(705,374) .

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

Step 1: Since 645 > 1, we apply the division lemma to 645 and 1, to get

645 = 1 x 645 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 645 is 1

Notice that 1 = HCF(645,1) .

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Frequently Asked Questions on HCF of 705, 374, 645 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 705, 374, 645?

Answer: HCF of 705, 374, 645 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 705, 374, 645 using Euclid's Algorithm?

Answer: For arbitrary numbers 705, 374, 645 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.