Highest Common Factor of 565, 414, 562 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 565, 414, 562 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 565, 414, 562 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 565, 414, 562 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 565, 414, 562 is 1.

HCF(565, 414, 562) = 1

HCF of 565, 414, 562 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 565, 414, 562 is 1.

Highest Common Factor of 565,414,562 using Euclid's algorithm

Highest Common Factor of 565,414,562 is 1

Step 1: Since 565 > 414, we apply the division lemma to 565 and 414, to get

565 = 414 x 1 + 151

Step 2: Since the reminder 414 ≠ 0, we apply division lemma to 151 and 414, to get

414 = 151 x 2 + 112

Step 3: We consider the new divisor 151 and the new remainder 112, and apply the division lemma to get

151 = 112 x 1 + 39

We consider the new divisor 112 and the new remainder 39,and apply the division lemma to get

112 = 39 x 2 + 34

We consider the new divisor 39 and the new remainder 34,and apply the division lemma to get

39 = 34 x 1 + 5

We consider the new divisor 34 and the new remainder 5,and apply the division lemma to get

34 = 5 x 6 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 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 565 and 414 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(34,5) = HCF(39,34) = HCF(112,39) = HCF(151,112) = HCF(414,151) = HCF(565,414) .

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

Step 1: Since 562 > 1, we apply the division lemma to 562 and 1, to get

562 = 1 x 562 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 562 is 1

Notice that 1 = HCF(562,1) .

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Frequently Asked Questions on HCF of 565, 414, 562 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 565, 414, 562?

Answer: HCF of 565, 414, 562 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 565, 414, 562 using Euclid's Algorithm?

Answer: For arbitrary numbers 565, 414, 562 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.