Highest Common Factor of 565, 990, 142 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, 990, 142 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 565, 990, 142 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, 990, 142 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, 990, 142 is 1.

HCF(565, 990, 142) = 1

HCF of 565, 990, 142 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, 990, 142 is 1.

Highest Common Factor of 565,990,142 using Euclid's algorithm

Highest Common Factor of 565,990,142 is 1

Step 1: Since 990 > 565, we apply the division lemma to 990 and 565, to get

990 = 565 x 1 + 425

Step 2: Since the reminder 565 ≠ 0, we apply division lemma to 425 and 565, to get

565 = 425 x 1 + 140

Step 3: We consider the new divisor 425 and the new remainder 140, and apply the division lemma to get

425 = 140 x 3 + 5

We consider the new divisor 140 and the new remainder 5, and apply the division lemma to get

140 = 5 x 28 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 565 and 990 is 5

Notice that 5 = HCF(140,5) = HCF(425,140) = HCF(565,425) = HCF(990,565) .

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

Step 1: Since 142 > 5, we apply the division lemma to 142 and 5, to get

142 = 5 x 28 + 2

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 2 and 5, to get

5 = 2 x 2 + 1

Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma 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 5 and 142 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(142,5) .

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Frequently Asked Questions on HCF of 565, 990, 142 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, 990, 142?

Answer: HCF of 565, 990, 142 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 565, 990, 142 using Euclid's Algorithm?

Answer: For arbitrary numbers 565, 990, 142 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.