Highest Common Factor of 577, 969, 906 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 577, 969, 906 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 577, 969, 906 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 577, 969, 906 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 577, 969, 906 is 1.

HCF(577, 969, 906) = 1

HCF of 577, 969, 906 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 577, 969, 906 is 1.

Highest Common Factor of 577,969,906 using Euclid's algorithm

Highest Common Factor of 577,969,906 is 1

Step 1: Since 969 > 577, we apply the division lemma to 969 and 577, to get

969 = 577 x 1 + 392

Step 2: Since the reminder 577 ≠ 0, we apply division lemma to 392 and 577, to get

577 = 392 x 1 + 185

Step 3: We consider the new divisor 392 and the new remainder 185, and apply the division lemma to get

392 = 185 x 2 + 22

We consider the new divisor 185 and the new remainder 22,and apply the division lemma to get

185 = 22 x 8 + 9

We consider the new divisor 22 and the new remainder 9,and apply the division lemma to get

22 = 9 x 2 + 4

We consider the new divisor 9 and the new remainder 4,and apply the division lemma to get

9 = 4 x 2 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 577 and 969 is 1

Notice that 1 = HCF(4,1) = HCF(9,4) = HCF(22,9) = HCF(185,22) = HCF(392,185) = HCF(577,392) = HCF(969,577) .

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

Step 1: Since 906 > 1, we apply the division lemma to 906 and 1, to get

906 = 1 x 906 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 906 is 1

Notice that 1 = HCF(906,1) .

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Frequently Asked Questions on HCF of 577, 969, 906 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 577, 969, 906?

Answer: HCF of 577, 969, 906 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 577, 969, 906 using Euclid's Algorithm?

Answer: For arbitrary numbers 577, 969, 906 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.