Highest Common Factor of 780, 295, 109 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 780, 295, 109 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 780, 295, 109 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 780, 295, 109 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 780, 295, 109 is 1.

HCF(780, 295, 109) = 1

HCF of 780, 295, 109 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 780, 295, 109 is 1.

Highest Common Factor of 780,295,109 using Euclid's algorithm

Highest Common Factor of 780,295,109 is 1

Step 1: Since 780 > 295, we apply the division lemma to 780 and 295, to get

780 = 295 x 2 + 190

Step 2: Since the reminder 295 ≠ 0, we apply division lemma to 190 and 295, to get

295 = 190 x 1 + 105

Step 3: We consider the new divisor 190 and the new remainder 105, and apply the division lemma to get

190 = 105 x 1 + 85

We consider the new divisor 105 and the new remainder 85,and apply the division lemma to get

105 = 85 x 1 + 20

We consider the new divisor 85 and the new remainder 20,and apply the division lemma to get

85 = 20 x 4 + 5

We consider the new divisor 20 and the new remainder 5,and apply the division lemma to get

20 = 5 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 780 and 295 is 5

Notice that 5 = HCF(20,5) = HCF(85,20) = HCF(105,85) = HCF(190,105) = HCF(295,190) = HCF(780,295) .

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

Step 1: Since 109 > 5, we apply the division lemma to 109 and 5, to get

109 = 5 x 21 + 4

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 4 and 5, to get

5 = 4 x 1 + 1

Step 3: We consider the new divisor 4 and the new remainder 1, and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5 and 109 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(109,5) .

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Frequently Asked Questions on HCF of 780, 295, 109 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 780, 295, 109?

Answer: HCF of 780, 295, 109 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 780, 295, 109 using Euclid's Algorithm?

Answer: For arbitrary numbers 780, 295, 109 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.