Highest Common Factor of 564, 358, 37 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, 358, 37 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 564, 358, 37 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, 358, 37 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, 358, 37 is 1.

HCF(564, 358, 37) = 1

HCF of 564, 358, 37 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, 358, 37 is 1.

Highest Common Factor of 564,358,37 using Euclid's algorithm

Highest Common Factor of 564,358,37 is 1

Step 1: Since 564 > 358, we apply the division lemma to 564 and 358, to get

564 = 358 x 1 + 206

Step 2: Since the reminder 358 ≠ 0, we apply division lemma to 206 and 358, to get

358 = 206 x 1 + 152

Step 3: We consider the new divisor 206 and the new remainder 152, and apply the division lemma to get

206 = 152 x 1 + 54

We consider the new divisor 152 and the new remainder 54,and apply the division lemma to get

152 = 54 x 2 + 44

We consider the new divisor 54 and the new remainder 44,and apply the division lemma to get

54 = 44 x 1 + 10

We consider the new divisor 44 and the new remainder 10,and apply the division lemma to get

44 = 10 x 4 + 4

We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get

10 = 4 x 2 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 564 and 358 is 2

Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(44,10) = HCF(54,44) = HCF(152,54) = HCF(206,152) = HCF(358,206) = HCF(564,358) .

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

Step 1: Since 37 > 2, we apply the division lemma to 37 and 2, to get

37 = 2 x 18 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 37 is 1

Notice that 1 = HCF(2,1) = HCF(37,2) .

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Frequently Asked Questions on HCF of 564, 358, 37 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, 358, 37?

Answer: HCF of 564, 358, 37 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 564, 358, 37 using Euclid's Algorithm?

Answer: For arbitrary numbers 564, 358, 37 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.