Highest Common Factor of 902, 749, 249 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, 749, 249 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 902, 749, 249 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, 749, 249 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, 749, 249 is 1.

HCF(902, 749, 249) = 1

HCF of 902, 749, 249 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, 749, 249 is 1.

Highest Common Factor of 902,749,249 using Euclid's algorithm

Highest Common Factor of 902,749,249 is 1

Step 1: Since 902 > 749, we apply the division lemma to 902 and 749, to get

902 = 749 x 1 + 153

Step 2: Since the reminder 749 ≠ 0, we apply division lemma to 153 and 749, to get

749 = 153 x 4 + 137

Step 3: We consider the new divisor 153 and the new remainder 137, and apply the division lemma to get

153 = 137 x 1 + 16

We consider the new divisor 137 and the new remainder 16,and apply the division lemma to get

137 = 16 x 8 + 9

We consider the new divisor 16 and the new remainder 9,and apply the division lemma to get

16 = 9 x 1 + 7

We consider the new divisor 9 and the new remainder 7,and apply the division lemma to get

9 = 7 x 1 + 2

We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get

7 = 2 x 3 + 1

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 902 and 749 is 1

Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(9,7) = HCF(16,9) = HCF(137,16) = HCF(153,137) = HCF(749,153) = HCF(902,749) .

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

Step 1: Since 249 > 1, we apply the division lemma to 249 and 1, to get

249 = 1 x 249 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 249 is 1

Notice that 1 = HCF(249,1) .

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Frequently Asked Questions on HCF of 902, 749, 249 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, 749, 249?

Answer: HCF of 902, 749, 249 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 902, 749, 249 using Euclid's Algorithm?

Answer: For arbitrary numbers 902, 749, 249 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.