Highest Common Factor of 344, 528, 164 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 344, 528, 164 i.e. 4 the largest integer that leaves a remainder zero for all numbers.

HCF of 344, 528, 164 is 4 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 344, 528, 164 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 344, 528, 164 is 4.

HCF(344, 528, 164) = 4

HCF of 344, 528, 164 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 344, 528, 164 is 4.

Highest Common Factor of 344,528,164 using Euclid's algorithm

Highest Common Factor of 344,528,164 is 4

Step 1: Since 528 > 344, we apply the division lemma to 528 and 344, to get

528 = 344 x 1 + 184

Step 2: Since the reminder 344 ≠ 0, we apply division lemma to 184 and 344, to get

344 = 184 x 1 + 160

Step 3: We consider the new divisor 184 and the new remainder 160, and apply the division lemma to get

184 = 160 x 1 + 24

We consider the new divisor 160 and the new remainder 24,and apply the division lemma to get

160 = 24 x 6 + 16

We consider the new divisor 24 and the new remainder 16,and apply the division lemma to get

24 = 16 x 1 + 8

We consider the new divisor 16 and the new remainder 8,and apply the division lemma to get

16 = 8 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 344 and 528 is 8

Notice that 8 = HCF(16,8) = HCF(24,16) = HCF(160,24) = HCF(184,160) = HCF(344,184) = HCF(528,344) .

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

Step 1: Since 164 > 8, we apply the division lemma to 164 and 8, to get

164 = 8 x 20 + 4

Step 2: Since the reminder 8 ≠ 0, we apply division lemma to 4 and 8, to get

8 = 4 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 8 and 164 is 4

Notice that 4 = HCF(8,4) = HCF(164,8) .

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Frequently Asked Questions on HCF of 344, 528, 164 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 344, 528, 164?

Answer: HCF of 344, 528, 164 is 4 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 344, 528, 164 using Euclid's Algorithm?

Answer: For arbitrary numbers 344, 528, 164 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.