Highest Common Factor of 342, 777, 47 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 342, 777, 47 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 342, 777, 47 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 342, 777, 47 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 342, 777, 47 is 1.

HCF(342, 777, 47) = 1

HCF of 342, 777, 47 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 342, 777, 47 is 1.

Highest Common Factor of 342,777,47 using Euclid's algorithm

Highest Common Factor of 342,777,47 is 1

Step 1: Since 777 > 342, we apply the division lemma to 777 and 342, to get

777 = 342 x 2 + 93

Step 2: Since the reminder 342 ≠ 0, we apply division lemma to 93 and 342, to get

342 = 93 x 3 + 63

Step 3: We consider the new divisor 93 and the new remainder 63, and apply the division lemma to get

93 = 63 x 1 + 30

We consider the new divisor 63 and the new remainder 30,and apply the division lemma to get

63 = 30 x 2 + 3

We consider the new divisor 30 and the new remainder 3,and apply the division lemma to get

30 = 3 x 10 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 342 and 777 is 3

Notice that 3 = HCF(30,3) = HCF(63,30) = HCF(93,63) = HCF(342,93) = HCF(777,342) .

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

Step 1: Since 47 > 3, we apply the division lemma to 47 and 3, to get

47 = 3 x 15 + 2

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

3 = 2 x 1 + 1

Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma 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 3 and 47 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(47,3) .

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Frequently Asked Questions on HCF of 342, 777, 47 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 342, 777, 47?

Answer: HCF of 342, 777, 47 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 342, 777, 47 using Euclid's Algorithm?

Answer: For arbitrary numbers 342, 777, 47 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.