Highest Common Factor of 463, 777, 345 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 463, 777, 345 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 463, 777, 345 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 463, 777, 345 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 463, 777, 345 is 1.

HCF(463, 777, 345) = 1

HCF of 463, 777, 345 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 463, 777, 345 is 1.

Highest Common Factor of 463,777,345 using Euclid's algorithm

Highest Common Factor of 463,777,345 is 1

Step 1: Since 777 > 463, we apply the division lemma to 777 and 463, to get

777 = 463 x 1 + 314

Step 2: Since the reminder 463 ≠ 0, we apply division lemma to 314 and 463, to get

463 = 314 x 1 + 149

Step 3: We consider the new divisor 314 and the new remainder 149, and apply the division lemma to get

314 = 149 x 2 + 16

We consider the new divisor 149 and the new remainder 16,and apply the division lemma to get

149 = 16 x 9 + 5

We consider the new divisor 16 and the new remainder 5,and apply the division lemma to get

16 = 5 x 3 + 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 463 and 777 is 1

Notice that 1 = HCF(5,1) = HCF(16,5) = HCF(149,16) = HCF(314,149) = HCF(463,314) = HCF(777,463) .

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

Step 1: Since 345 > 1, we apply the division lemma to 345 and 1, to get

345 = 1 x 345 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 345 is 1

Notice that 1 = HCF(345,1) .

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Frequently Asked Questions on HCF of 463, 777, 345 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 463, 777, 345?

Answer: HCF of 463, 777, 345 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 463, 777, 345 using Euclid's Algorithm?

Answer: For arbitrary numbers 463, 777, 345 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.