Highest Common Factor of 870, 242, 560, 827 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 870, 242, 560, 827 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 870, 242, 560, 827 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 870, 242, 560, 827 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 870, 242, 560, 827 is 1.

HCF(870, 242, 560, 827) = 1

HCF of 870, 242, 560, 827 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 870, 242, 560, 827 is 1.

Highest Common Factor of 870,242,560,827 using Euclid's algorithm

Highest Common Factor of 870,242,560,827 is 1

Step 1: Since 870 > 242, we apply the division lemma to 870 and 242, to get

870 = 242 x 3 + 144

Step 2: Since the reminder 242 ≠ 0, we apply division lemma to 144 and 242, to get

242 = 144 x 1 + 98

Step 3: We consider the new divisor 144 and the new remainder 98, and apply the division lemma to get

144 = 98 x 1 + 46

We consider the new divisor 98 and the new remainder 46,and apply the division lemma to get

98 = 46 x 2 + 6

We consider the new divisor 46 and the new remainder 6,and apply the division lemma to get

46 = 6 x 7 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 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 870 and 242 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(46,6) = HCF(98,46) = HCF(144,98) = HCF(242,144) = HCF(870,242) .

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

Step 1: Since 560 > 2, we apply the division lemma to 560 and 2, to get

560 = 2 x 280 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 560 is 2

Notice that 2 = HCF(560,2) .

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

Step 1: Since 827 > 2, we apply the division lemma to 827 and 2, to get

827 = 2 x 413 + 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 827 is 1

Notice that 1 = HCF(2,1) = HCF(827,2) .

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Frequently Asked Questions on HCF of 870, 242, 560, 827 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 870, 242, 560, 827?

Answer: HCF of 870, 242, 560, 827 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 870, 242, 560, 827 using Euclid's Algorithm?

Answer: For arbitrary numbers 870, 242, 560, 827 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.