Highest Common Factor of 705, 577, 777 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 705, 577, 777 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 705, 577, 777 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 705, 577, 777 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 705, 577, 777 is 1.

HCF(705, 577, 777) = 1

HCF of 705, 577, 777 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 705, 577, 777 is 1.

Highest Common Factor of 705,577,777 using Euclid's algorithm

Highest Common Factor of 705,577,777 is 1

Step 1: Since 705 > 577, we apply the division lemma to 705 and 577, to get

705 = 577 x 1 + 128

Step 2: Since the reminder 577 ≠ 0, we apply division lemma to 128 and 577, to get

577 = 128 x 4 + 65

Step 3: We consider the new divisor 128 and the new remainder 65, and apply the division lemma to get

128 = 65 x 1 + 63

We consider the new divisor 65 and the new remainder 63,and apply the division lemma to get

65 = 63 x 1 + 2

We consider the new divisor 63 and the new remainder 2,and apply the division lemma to get

63 = 2 x 31 + 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 705 and 577 is 1

Notice that 1 = HCF(2,1) = HCF(63,2) = HCF(65,63) = HCF(128,65) = HCF(577,128) = HCF(705,577) .

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

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

777 = 1 x 777 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 777 is 1

Notice that 1 = HCF(777,1) .

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Frequently Asked Questions on HCF of 705, 577, 777 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 705, 577, 777?

Answer: HCF of 705, 577, 777 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 705, 577, 777 using Euclid's Algorithm?

Answer: For arbitrary numbers 705, 577, 777 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.