Highest Common Factor of 354, 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 354, 645 i.e. 3 the largest integer that leaves a remainder zero for all numbers.

HCF of 354, 645 is 3 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 354, 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 354, 645 is 3.

HCF(354, 645) = 3

HCF of 354, 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 354, 645 is 3.

Highest Common Factor of 354,645 using Euclid's algorithm

Highest Common Factor of 354,645 is 3

Step 1: Since 645 > 354, we apply the division lemma to 645 and 354, to get

645 = 354 x 1 + 291

Step 2: Since the reminder 354 ≠ 0, we apply division lemma to 291 and 354, to get

354 = 291 x 1 + 63

Step 3: We consider the new divisor 291 and the new remainder 63, and apply the division lemma to get

291 = 63 x 4 + 39

We consider the new divisor 63 and the new remainder 39,and apply the division lemma to get

63 = 39 x 1 + 24

We consider the new divisor 39 and the new remainder 24,and apply the division lemma to get

39 = 24 x 1 + 15

We consider the new divisor 24 and the new remainder 15,and apply the division lemma to get

24 = 15 x 1 + 9

We consider the new divisor 15 and the new remainder 9,and apply the division lemma to get

15 = 9 x 1 + 6

We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get

9 = 6 x 1 + 3

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

6 = 3 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 354 and 645 is 3

Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(15,9) = HCF(24,15) = HCF(39,24) = HCF(63,39) = HCF(291,63) = HCF(354,291) = HCF(645,354) .

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Frequently Asked Questions on HCF of 354, 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 354, 645?

Answer: HCF of 354, 645 is 3 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 354, 645 using Euclid's Algorithm?

Answer: For arbitrary numbers 354, 645 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.