Highest Common Factor of 561, 925, 64 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 561, 925, 64 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 561, 925, 64 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 561, 925, 64 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 561, 925, 64 is 1.

HCF(561, 925, 64) = 1

HCF of 561, 925, 64 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 561, 925, 64 is 1.

Highest Common Factor of 561,925,64 using Euclid's algorithm

Highest Common Factor of 561,925,64 is 1

Step 1: Since 925 > 561, we apply the division lemma to 925 and 561, to get

925 = 561 x 1 + 364

Step 2: Since the reminder 561 ≠ 0, we apply division lemma to 364 and 561, to get

561 = 364 x 1 + 197

Step 3: We consider the new divisor 364 and the new remainder 197, and apply the division lemma to get

364 = 197 x 1 + 167

We consider the new divisor 197 and the new remainder 167,and apply the division lemma to get

197 = 167 x 1 + 30

We consider the new divisor 167 and the new remainder 30,and apply the division lemma to get

167 = 30 x 5 + 17

We consider the new divisor 30 and the new remainder 17,and apply the division lemma to get

30 = 17 x 1 + 13

We consider the new divisor 17 and the new remainder 13,and apply the division lemma to get

17 = 13 x 1 + 4

We consider the new divisor 13 and the new remainder 4,and apply the division lemma to get

13 = 4 x 3 + 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 561 and 925 is 1

Notice that 1 = HCF(4,1) = HCF(13,4) = HCF(17,13) = HCF(30,17) = HCF(167,30) = HCF(197,167) = HCF(364,197) = HCF(561,364) = HCF(925,561) .

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

Step 1: Since 64 > 1, we apply the division lemma to 64 and 1, to get

64 = 1 x 64 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 64 is 1

Notice that 1 = HCF(64,1) .

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Frequently Asked Questions on HCF of 561, 925, 64 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 561, 925, 64?

Answer: HCF of 561, 925, 64 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 561, 925, 64 using Euclid's Algorithm?

Answer: For arbitrary numbers 561, 925, 64 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.