Highest Common Factor of 354, 848, 163 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, 848, 163 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 354, 848, 163 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 354, 848, 163 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, 848, 163 is 1.

HCF(354, 848, 163) = 1

HCF of 354, 848, 163 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, 848, 163 is 1.

Highest Common Factor of 354,848,163 using Euclid's algorithm

Highest Common Factor of 354,848,163 is 1

Step 1: Since 848 > 354, we apply the division lemma to 848 and 354, to get

848 = 354 x 2 + 140

Step 2: Since the reminder 354 ≠ 0, we apply division lemma to 140 and 354, to get

354 = 140 x 2 + 74

Step 3: We consider the new divisor 140 and the new remainder 74, and apply the division lemma to get

140 = 74 x 1 + 66

We consider the new divisor 74 and the new remainder 66,and apply the division lemma to get

74 = 66 x 1 + 8

We consider the new divisor 66 and the new remainder 8,and apply the division lemma to get

66 = 8 x 8 + 2

We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get

8 = 2 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 354 and 848 is 2

Notice that 2 = HCF(8,2) = HCF(66,8) = HCF(74,66) = HCF(140,74) = HCF(354,140) = HCF(848,354) .

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

Step 1: Since 163 > 2, we apply the division lemma to 163 and 2, to get

163 = 2 x 81 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 163 is 1

Notice that 1 = HCF(2,1) = HCF(163,2) .

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Frequently Asked Questions on HCF of 354, 848, 163 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, 848, 163?

Answer: HCF of 354, 848, 163 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 354, 848, 163 using Euclid's Algorithm?

Answer: For arbitrary numbers 354, 848, 163 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.