Highest Common Factor of 357, 102 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, 102 i.e. 51 the largest integer that leaves a remainder zero for all numbers.

HCF of 357, 102 is 51 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, 102 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, 102 is 51.

HCF(357, 102) = 51

HCF of 357, 102 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 357, 102 is 51.

Highest Common Factor of 357,102 using Euclid's algorithm

Highest Common Factor of 357,102 is 51

Step 1: Since 357 > 102, we apply the division lemma to 357 and 102, to get

357 = 102 x 3 + 51

Step 2: Since the reminder 102 ≠ 0, we apply division lemma to 51 and 102, to get

102 = 51 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 51, the HCF of 357 and 102 is 51

Notice that 51 = HCF(102,51) = HCF(357,102) .

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Frequently Asked Questions on HCF of 357, 102 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, 102?

Answer: HCF of 357, 102 is 51 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 357, 102 using Euclid's Algorithm?

Answer: For arbitrary numbers 357, 102 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.