Highest Common Factor of 496, 785, 357 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 496, 785, 357 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 496, 785, 357 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 496, 785, 357 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 496, 785, 357 is 1.

HCF(496, 785, 357) = 1

HCF of 496, 785, 357 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 496, 785, 357 is 1.

Highest Common Factor of 496,785,357 using Euclid's algorithm

Highest Common Factor of 496,785,357 is 1

Step 1: Since 785 > 496, we apply the division lemma to 785 and 496, to get

785 = 496 x 1 + 289

Step 2: Since the reminder 496 ≠ 0, we apply division lemma to 289 and 496, to get

496 = 289 x 1 + 207

Step 3: We consider the new divisor 289 and the new remainder 207, and apply the division lemma to get

289 = 207 x 1 + 82

We consider the new divisor 207 and the new remainder 82,and apply the division lemma to get

207 = 82 x 2 + 43

We consider the new divisor 82 and the new remainder 43,and apply the division lemma to get

82 = 43 x 1 + 39

We consider the new divisor 43 and the new remainder 39,and apply the division lemma to get

43 = 39 x 1 + 4

We consider the new divisor 39 and the new remainder 4,and apply the division lemma to get

39 = 4 x 9 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 496 and 785 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(39,4) = HCF(43,39) = HCF(82,43) = HCF(207,82) = HCF(289,207) = HCF(496,289) = HCF(785,496) .

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

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

357 = 1 x 357 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 357 is 1

Notice that 1 = HCF(357,1) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 496, 785, 357 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 496, 785, 357?

Answer: HCF of 496, 785, 357 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 496, 785, 357 using Euclid's Algorithm?

Answer: For arbitrary numbers 496, 785, 357 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.