Highest Common Factor of 278, 470, 907 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 278, 470, 907 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 278, 470, 907 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 278, 470, 907 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 278, 470, 907 is 1.

HCF(278, 470, 907) = 1

HCF of 278, 470, 907 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 278, 470, 907 is 1.

Highest Common Factor of 278,470,907 using Euclid's algorithm

Highest Common Factor of 278,470,907 is 1

Step 1: Since 470 > 278, we apply the division lemma to 470 and 278, to get

470 = 278 x 1 + 192

Step 2: Since the reminder 278 ≠ 0, we apply division lemma to 192 and 278, to get

278 = 192 x 1 + 86

Step 3: We consider the new divisor 192 and the new remainder 86, and apply the division lemma to get

192 = 86 x 2 + 20

We consider the new divisor 86 and the new remainder 20,and apply the division lemma to get

86 = 20 x 4 + 6

We consider the new divisor 20 and the new remainder 6,and apply the division lemma to get

20 = 6 x 3 + 2

We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get

6 = 2 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 278 and 470 is 2

Notice that 2 = HCF(6,2) = HCF(20,6) = HCF(86,20) = HCF(192,86) = HCF(278,192) = HCF(470,278) .

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

Step 1: Since 907 > 2, we apply the division lemma to 907 and 2, to get

907 = 2 x 453 + 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 907 is 1

Notice that 1 = HCF(2,1) = HCF(907,2) .

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Frequently Asked Questions on HCF of 278, 470, 907 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 278, 470, 907?

Answer: HCF of 278, 470, 907 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 278, 470, 907 using Euclid's Algorithm?

Answer: For arbitrary numbers 278, 470, 907 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.