Highest Common Factor of 354, 208, 802 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, 208, 802 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 354, 208, 802 is 2 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, 208, 802 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, 208, 802 is 2.

HCF(354, 208, 802) = 2

HCF of 354, 208, 802 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, 208, 802 is 2.

Highest Common Factor of 354,208,802 using Euclid's algorithm

Highest Common Factor of 354,208,802 is 2

Step 1: Since 354 > 208, we apply the division lemma to 354 and 208, to get

354 = 208 x 1 + 146

Step 2: Since the reminder 208 ≠ 0, we apply division lemma to 146 and 208, to get

208 = 146 x 1 + 62

Step 3: We consider the new divisor 146 and the new remainder 62, and apply the division lemma to get

146 = 62 x 2 + 22

We consider the new divisor 62 and the new remainder 22,and apply the division lemma to get

62 = 22 x 2 + 18

We consider the new divisor 22 and the new remainder 18,and apply the division lemma to get

22 = 18 x 1 + 4

We consider the new divisor 18 and the new remainder 4,and apply the division lemma to get

18 = 4 x 4 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 354 and 208 is 2

Notice that 2 = HCF(4,2) = HCF(18,4) = HCF(22,18) = HCF(62,22) = HCF(146,62) = HCF(208,146) = HCF(354,208) .

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

Step 1: Since 802 > 2, we apply the division lemma to 802 and 2, to get

802 = 2 x 401 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 802 is 2

Notice that 2 = HCF(802,2) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 354, 208, 802 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, 208, 802?

Answer: HCF of 354, 208, 802 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 354, 208, 802 using Euclid's Algorithm?

Answer: For arbitrary numbers 354, 208, 802 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.