Highest Common Factor of 906, 157, 304 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 906, 157, 304 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 906, 157, 304 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 906, 157, 304 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 906, 157, 304 is 1.

HCF(906, 157, 304) = 1

HCF of 906, 157, 304 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 906, 157, 304 is 1.

Highest Common Factor of 906,157,304 using Euclid's algorithm

Highest Common Factor of 906,157,304 is 1

Step 1: Since 906 > 157, we apply the division lemma to 906 and 157, to get

906 = 157 x 5 + 121

Step 2: Since the reminder 157 ≠ 0, we apply division lemma to 121 and 157, to get

157 = 121 x 1 + 36

Step 3: We consider the new divisor 121 and the new remainder 36, and apply the division lemma to get

121 = 36 x 3 + 13

We consider the new divisor 36 and the new remainder 13,and apply the division lemma to get

36 = 13 x 2 + 10

We consider the new divisor 13 and the new remainder 10,and apply the division lemma to get

13 = 10 x 1 + 3

We consider the new divisor 10 and the new remainder 3,and apply the division lemma to get

10 = 3 x 3 + 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 906 and 157 is 1

Notice that 1 = HCF(3,1) = HCF(10,3) = HCF(13,10) = HCF(36,13) = HCF(121,36) = HCF(157,121) = HCF(906,157) .

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

Step 1: Since 304 > 1, we apply the division lemma to 304 and 1, to get

304 = 1 x 304 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 304 is 1

Notice that 1 = HCF(304,1) .

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Frequently Asked Questions on HCF of 906, 157, 304 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 906, 157, 304?

Answer: HCF of 906, 157, 304 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 906, 157, 304 using Euclid's Algorithm?

Answer: For arbitrary numbers 906, 157, 304 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.