Highest Common Factor of 357, 1629, 5951 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 357, 1629, 5951 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 357, 1629, 5951 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 357, 1629, 5951 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 357, 1629, 5951 is 1.

HCF(357, 1629, 5951) = 1

HCF of 357, 1629, 5951 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 357, 1629, 5951 is 1.

Highest Common Factor of 357,1629,5951 using Euclid's algorithm

Highest Common Factor of 357,1629,5951 is 1

Step 1: Since 1629 > 357, we apply the division lemma to 1629 and 357, to get

1629 = 357 x 4 + 201

Step 2: Since the reminder 357 ≠ 0, we apply division lemma to 201 and 357, to get

357 = 201 x 1 + 156

Step 3: We consider the new divisor 201 and the new remainder 156, and apply the division lemma to get

201 = 156 x 1 + 45

We consider the new divisor 156 and the new remainder 45,and apply the division lemma to get

156 = 45 x 3 + 21

We consider the new divisor 45 and the new remainder 21,and apply the division lemma to get

45 = 21 x 2 + 3

We consider the new divisor 21 and the new remainder 3,and apply the division lemma to get

21 = 3 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 357 and 1629 is 3

Notice that 3 = HCF(21,3) = HCF(45,21) = HCF(156,45) = HCF(201,156) = HCF(357,201) = HCF(1629,357) .

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

Step 1: Since 5951 > 3, we apply the division lemma to 5951 and 3, to get

5951 = 3 x 1983 + 2

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get

3 = 2 x 1 + 1

Step 3: 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 3 and 5951 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5951,3) .

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Frequently Asked Questions on HCF of 357, 1629, 5951 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 357, 1629, 5951?

Answer: HCF of 357, 1629, 5951 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 357, 1629, 5951 using Euclid's Algorithm?

Answer: For arbitrary numbers 357, 1629, 5951 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.