Highest Common Factor of 310, 780, 357 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 310, 780, 357 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 310, 780, 357 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 310, 780, 357 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 310, 780, 357 is 1.

HCF(310, 780, 357) = 1

HCF of 310, 780, 357 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 310, 780, 357 is 1.

Highest Common Factor of 310,780,357 using Euclid's algorithm

Highest Common Factor of 310,780,357 is 1

Step 1: Since 780 > 310, we apply the division lemma to 780 and 310, to get

780 = 310 x 2 + 160

Step 2: Since the reminder 310 ≠ 0, we apply division lemma to 160 and 310, to get

310 = 160 x 1 + 150

Step 3: We consider the new divisor 160 and the new remainder 150, and apply the division lemma to get

160 = 150 x 1 + 10

We consider the new divisor 150 and the new remainder 10, and apply the division lemma to get

150 = 10 x 15 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 310 and 780 is 10

Notice that 10 = HCF(150,10) = HCF(160,150) = HCF(310,160) = HCF(780,310) .

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

Step 1: Since 357 > 10, we apply the division lemma to 357 and 10, to get

357 = 10 x 35 + 7

Step 2: Since the reminder 10 ≠ 0, we apply division lemma to 7 and 10, to get

10 = 7 x 1 + 3

Step 3: We consider the new divisor 7 and the new remainder 3, and apply the division lemma to get

7 = 3 x 2 + 1

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

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 10 and 357 is 1

Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(10,7) = HCF(357,10) .

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Frequently Asked Questions on HCF of 310, 780, 357 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 310, 780, 357?

Answer: HCF of 310, 780, 357 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 310, 780, 357 using Euclid's Algorithm?

Answer: For arbitrary numbers 310, 780, 357 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.