Highest Common Factor of 849, 524, 137 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 849, 524, 137 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 849, 524, 137 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 849, 524, 137 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 849, 524, 137 is 1.

HCF(849, 524, 137) = 1

HCF of 849, 524, 137 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 849, 524, 137 is 1.

Highest Common Factor of 849,524,137 using Euclid's algorithm

Highest Common Factor of 849,524,137 is 1

Step 1: Since 849 > 524, we apply the division lemma to 849 and 524, to get

849 = 524 x 1 + 325

Step 2: Since the reminder 524 ≠ 0, we apply division lemma to 325 and 524, to get

524 = 325 x 1 + 199

Step 3: We consider the new divisor 325 and the new remainder 199, and apply the division lemma to get

325 = 199 x 1 + 126

We consider the new divisor 199 and the new remainder 126,and apply the division lemma to get

199 = 126 x 1 + 73

We consider the new divisor 126 and the new remainder 73,and apply the division lemma to get

126 = 73 x 1 + 53

We consider the new divisor 73 and the new remainder 53,and apply the division lemma to get

73 = 53 x 1 + 20

We consider the new divisor 53 and the new remainder 20,and apply the division lemma to get

53 = 20 x 2 + 13

We consider the new divisor 20 and the new remainder 13,and apply the division lemma to get

20 = 13 x 1 + 7

We consider the new divisor 13 and the new remainder 7,and apply the division lemma to get

13 = 7 x 1 + 6

We consider the new divisor 7 and the new remainder 6,and apply the division lemma to get

7 = 6 x 1 + 1

We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get

6 = 1 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 849 and 524 is 1

Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(13,7) = HCF(20,13) = HCF(53,20) = HCF(73,53) = HCF(126,73) = HCF(199,126) = HCF(325,199) = HCF(524,325) = HCF(849,524) .

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

Step 1: Since 137 > 1, we apply the division lemma to 137 and 1, to get

137 = 1 x 137 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 137 is 1

Notice that 1 = HCF(137,1) .

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Frequently Asked Questions on HCF of 849, 524, 137 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 849, 524, 137?

Answer: HCF of 849, 524, 137 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 849, 524, 137 using Euclid's Algorithm?

Answer: For arbitrary numbers 849, 524, 137 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.