Highest Common Factor of 763, 300, 705 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 763, 300, 705 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 763, 300, 705 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 763, 300, 705 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 763, 300, 705 is 1.

HCF(763, 300, 705) = 1

HCF of 763, 300, 705 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 763, 300, 705 is 1.

Highest Common Factor of 763,300,705 using Euclid's algorithm

Highest Common Factor of 763,300,705 is 1

Step 1: Since 763 > 300, we apply the division lemma to 763 and 300, to get

763 = 300 x 2 + 163

Step 2: Since the reminder 300 ≠ 0, we apply division lemma to 163 and 300, to get

300 = 163 x 1 + 137

Step 3: We consider the new divisor 163 and the new remainder 137, and apply the division lemma to get

163 = 137 x 1 + 26

We consider the new divisor 137 and the new remainder 26,and apply the division lemma to get

137 = 26 x 5 + 7

We consider the new divisor 26 and the new remainder 7,and apply the division lemma to get

26 = 7 x 3 + 5

We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get

7 = 5 x 1 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 1

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 763 and 300 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(26,7) = HCF(137,26) = HCF(163,137) = HCF(300,163) = HCF(763,300) .

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

Step 1: Since 705 > 1, we apply the division lemma to 705 and 1, to get

705 = 1 x 705 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 705 is 1

Notice that 1 = HCF(705,1) .

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Frequently Asked Questions on HCF of 763, 300, 705 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 763, 300, 705?

Answer: HCF of 763, 300, 705 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 763, 300, 705 using Euclid's Algorithm?

Answer: For arbitrary numbers 763, 300, 705 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.