Highest Common Factor of 355, 924 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 355, 924 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 355, 924 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 355, 924 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 355, 924 is 1.

HCF(355, 924) = 1

HCF of 355, 924 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 355, 924 is 1.

Highest Common Factor of 355,924 using Euclid's algorithm

Highest Common Factor of 355,924 is 1

Step 1: Since 924 > 355, we apply the division lemma to 924 and 355, to get

924 = 355 x 2 + 214

Step 2: Since the reminder 355 ≠ 0, we apply division lemma to 214 and 355, to get

355 = 214 x 1 + 141

Step 3: We consider the new divisor 214 and the new remainder 141, and apply the division lemma to get

214 = 141 x 1 + 73

We consider the new divisor 141 and the new remainder 73,and apply the division lemma to get

141 = 73 x 1 + 68

We consider the new divisor 73 and the new remainder 68,and apply the division lemma to get

73 = 68 x 1 + 5

We consider the new divisor 68 and the new remainder 5,and apply the division lemma to get

68 = 5 x 13 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 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 355 and 924 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(68,5) = HCF(73,68) = HCF(141,73) = HCF(214,141) = HCF(355,214) = HCF(924,355) .

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Frequently Asked Questions on HCF of 355, 924 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 355, 924?

Answer: HCF of 355, 924 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 355, 924 using Euclid's Algorithm?

Answer: For arbitrary numbers 355, 924 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.