Highest Common Factor of 564, 149, 664 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 564, 149, 664 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 564, 149, 664 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 564, 149, 664 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 564, 149, 664 is 1.

HCF(564, 149, 664) = 1

HCF of 564, 149, 664 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 564, 149, 664 is 1.

Highest Common Factor of 564,149,664 using Euclid's algorithm

Highest Common Factor of 564,149,664 is 1

Step 1: Since 564 > 149, we apply the division lemma to 564 and 149, to get

564 = 149 x 3 + 117

Step 2: Since the reminder 149 ≠ 0, we apply division lemma to 117 and 149, to get

149 = 117 x 1 + 32

Step 3: We consider the new divisor 117 and the new remainder 32, and apply the division lemma to get

117 = 32 x 3 + 21

We consider the new divisor 32 and the new remainder 21,and apply the division lemma to get

32 = 21 x 1 + 11

We consider the new divisor 21 and the new remainder 11,and apply the division lemma to get

21 = 11 x 1 + 10

We consider the new divisor 11 and the new remainder 10,and apply the division lemma to get

11 = 10 x 1 + 1

We consider the new divisor 10 and the new remainder 1,and apply the division lemma to get

10 = 1 x 10 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 564 and 149 is 1

Notice that 1 = HCF(10,1) = HCF(11,10) = HCF(21,11) = HCF(32,21) = HCF(117,32) = HCF(149,117) = HCF(564,149) .

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

Step 1: Since 664 > 1, we apply the division lemma to 664 and 1, to get

664 = 1 x 664 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 664 is 1

Notice that 1 = HCF(664,1) .

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Frequently Asked Questions on HCF of 564, 149, 664 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 564, 149, 664?

Answer: HCF of 564, 149, 664 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 564, 149, 664 using Euclid's Algorithm?

Answer: For arbitrary numbers 564, 149, 664 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.