Highest Common Factor of 512, 850, 119 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 512, 850, 119 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 512, 850, 119 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 512, 850, 119 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 512, 850, 119 is 1.

HCF(512, 850, 119) = 1

HCF of 512, 850, 119 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 512, 850, 119 is 1.

Highest Common Factor of 512,850,119 using Euclid's algorithm

Highest Common Factor of 512,850,119 is 1

Step 1: Since 850 > 512, we apply the division lemma to 850 and 512, to get

850 = 512 x 1 + 338

Step 2: Since the reminder 512 ≠ 0, we apply division lemma to 338 and 512, to get

512 = 338 x 1 + 174

Step 3: We consider the new divisor 338 and the new remainder 174, and apply the division lemma to get

338 = 174 x 1 + 164

We consider the new divisor 174 and the new remainder 164,and apply the division lemma to get

174 = 164 x 1 + 10

We consider the new divisor 164 and the new remainder 10,and apply the division lemma to get

164 = 10 x 16 + 4

We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get

10 = 4 x 2 + 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 512 and 850 is 2

Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(164,10) = HCF(174,164) = HCF(338,174) = HCF(512,338) = HCF(850,512) .

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

Step 1: Since 119 > 2, we apply the division lemma to 119 and 2, to get

119 = 2 x 59 + 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 119 is 1

Notice that 1 = HCF(2,1) = HCF(119,2) .

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Frequently Asked Questions on HCF of 512, 850, 119 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 512, 850, 119?

Answer: HCF of 512, 850, 119 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 512, 850, 119 using Euclid's Algorithm?

Answer: For arbitrary numbers 512, 850, 119 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.