Highest Common Factor of 807, 456, 478 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 807, 456, 478 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 807, 456, 478 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 807, 456, 478 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 807, 456, 478 is 1.

HCF(807, 456, 478) = 1

HCF of 807, 456, 478 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 807, 456, 478 is 1.

Highest Common Factor of 807,456,478 using Euclid's algorithm

Highest Common Factor of 807,456,478 is 1

Step 1: Since 807 > 456, we apply the division lemma to 807 and 456, to get

807 = 456 x 1 + 351

Step 2: Since the reminder 456 ≠ 0, we apply division lemma to 351 and 456, to get

456 = 351 x 1 + 105

Step 3: We consider the new divisor 351 and the new remainder 105, and apply the division lemma to get

351 = 105 x 3 + 36

We consider the new divisor 105 and the new remainder 36,and apply the division lemma to get

105 = 36 x 2 + 33

We consider the new divisor 36 and the new remainder 33,and apply the division lemma to get

36 = 33 x 1 + 3

We consider the new divisor 33 and the new remainder 3,and apply the division lemma to get

33 = 3 x 11 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 807 and 456 is 3

Notice that 3 = HCF(33,3) = HCF(36,33) = HCF(105,36) = HCF(351,105) = HCF(456,351) = HCF(807,456) .

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

Step 1: Since 478 > 3, we apply the division lemma to 478 and 3, to get

478 = 3 x 159 + 1

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, 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 3 and 478 is 1

Notice that 1 = HCF(3,1) = HCF(478,3) .

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Frequently Asked Questions on HCF of 807, 456, 478 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 807, 456, 478?

Answer: HCF of 807, 456, 478 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 807, 456, 478 using Euclid's Algorithm?

Answer: For arbitrary numbers 807, 456, 478 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.