Highest Common Factor of 472, 775, 90 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 472, 775, 90 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 472, 775, 90 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 472, 775, 90 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 472, 775, 90 is 1.

HCF(472, 775, 90) = 1

HCF of 472, 775, 90 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 472, 775, 90 is 1.

Highest Common Factor of 472,775,90 using Euclid's algorithm

Highest Common Factor of 472,775,90 is 1

Step 1: Since 775 > 472, we apply the division lemma to 775 and 472, to get

775 = 472 x 1 + 303

Step 2: Since the reminder 472 ≠ 0, we apply division lemma to 303 and 472, to get

472 = 303 x 1 + 169

Step 3: We consider the new divisor 303 and the new remainder 169, and apply the division lemma to get

303 = 169 x 1 + 134

We consider the new divisor 169 and the new remainder 134,and apply the division lemma to get

169 = 134 x 1 + 35

We consider the new divisor 134 and the new remainder 35,and apply the division lemma to get

134 = 35 x 3 + 29

We consider the new divisor 35 and the new remainder 29,and apply the division lemma to get

35 = 29 x 1 + 6

We consider the new divisor 29 and the new remainder 6,and apply the division lemma to get

29 = 6 x 4 + 5

We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get

6 = 5 x 1 + 1

We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 472 and 775 is 1

Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(29,6) = HCF(35,29) = HCF(134,35) = HCF(169,134) = HCF(303,169) = HCF(472,303) = HCF(775,472) .

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

Step 1: Since 90 > 1, we apply the division lemma to 90 and 1, to get

90 = 1 x 90 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 90 is 1

Notice that 1 = HCF(90,1) .

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Frequently Asked Questions on HCF of 472, 775, 90 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 472, 775, 90?

Answer: HCF of 472, 775, 90 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 472, 775, 90 using Euclid's Algorithm?

Answer: For arbitrary numbers 472, 775, 90 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.