Highest Common Factor of 357, 9515, 9740 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 357, 9515, 9740 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 357, 9515, 9740 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 357, 9515, 9740 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 357, 9515, 9740 is 1.

HCF(357, 9515, 9740) = 1

HCF of 357, 9515, 9740 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 357, 9515, 9740 is 1.

Highest Common Factor of 357,9515,9740 using Euclid's algorithm

Highest Common Factor of 357,9515,9740 is 1

Step 1: Since 9515 > 357, we apply the division lemma to 9515 and 357, to get

9515 = 357 x 26 + 233

Step 2: Since the reminder 357 ≠ 0, we apply division lemma to 233 and 357, to get

357 = 233 x 1 + 124

Step 3: We consider the new divisor 233 and the new remainder 124, and apply the division lemma to get

233 = 124 x 1 + 109

We consider the new divisor 124 and the new remainder 109,and apply the division lemma to get

124 = 109 x 1 + 15

We consider the new divisor 109 and the new remainder 15,and apply the division lemma to get

109 = 15 x 7 + 4

We consider the new divisor 15 and the new remainder 4,and apply the division lemma to get

15 = 4 x 3 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 357 and 9515 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(15,4) = HCF(109,15) = HCF(124,109) = HCF(233,124) = HCF(357,233) = HCF(9515,357) .

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

Step 1: Since 9740 > 1, we apply the division lemma to 9740 and 1, to get

9740 = 1 x 9740 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 9740 is 1

Notice that 1 = HCF(9740,1) .

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Frequently Asked Questions on HCF of 357, 9515, 9740 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 357, 9515, 9740?

Answer: HCF of 357, 9515, 9740 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 357, 9515, 9740 using Euclid's Algorithm?

Answer: For arbitrary numbers 357, 9515, 9740 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.