Highest Common Factor of 902, 559, 960, 970 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 902, 559, 960, 970 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 902, 559, 960, 970 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 902, 559, 960, 970 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 902, 559, 960, 970 is 1.

HCF(902, 559, 960, 970) = 1

HCF of 902, 559, 960, 970 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 902, 559, 960, 970 is 1.

Highest Common Factor of 902,559,960,970 using Euclid's algorithm

Highest Common Factor of 902,559,960,970 is 1

Step 1: Since 902 > 559, we apply the division lemma to 902 and 559, to get

902 = 559 x 1 + 343

Step 2: Since the reminder 559 ≠ 0, we apply division lemma to 343 and 559, to get

559 = 343 x 1 + 216

Step 3: We consider the new divisor 343 and the new remainder 216, and apply the division lemma to get

343 = 216 x 1 + 127

We consider the new divisor 216 and the new remainder 127,and apply the division lemma to get

216 = 127 x 1 + 89

We consider the new divisor 127 and the new remainder 89,and apply the division lemma to get

127 = 89 x 1 + 38

We consider the new divisor 89 and the new remainder 38,and apply the division lemma to get

89 = 38 x 2 + 13

We consider the new divisor 38 and the new remainder 13,and apply the division lemma to get

38 = 13 x 2 + 12

We consider the new divisor 13 and the new remainder 12,and apply the division lemma to get

13 = 12 x 1 + 1

We consider the new divisor 12 and the new remainder 1,and apply the division lemma to get

12 = 1 x 12 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 902 and 559 is 1

Notice that 1 = HCF(12,1) = HCF(13,12) = HCF(38,13) = HCF(89,38) = HCF(127,89) = HCF(216,127) = HCF(343,216) = HCF(559,343) = HCF(902,559) .

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

Step 1: Since 960 > 1, we apply the division lemma to 960 and 1, to get

960 = 1 x 960 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 960 is 1

Notice that 1 = HCF(960,1) .

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

Step 1: Since 970 > 1, we apply the division lemma to 970 and 1, to get

970 = 1 x 970 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 970 is 1

Notice that 1 = HCF(970,1) .

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Frequently Asked Questions on HCF of 902, 559, 960, 970 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 902, 559, 960, 970?

Answer: HCF of 902, 559, 960, 970 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 902, 559, 960, 970 using Euclid's Algorithm?

Answer: For arbitrary numbers 902, 559, 960, 970 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.