Highest Common Factor of 753, 210, 117 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 753, 210, 117 i.e. 3 the largest integer that leaves a remainder zero for all numbers.

HCF of 753, 210, 117 is 3 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 753, 210, 117 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 753, 210, 117 is 3.

HCF(753, 210, 117) = 3

HCF of 753, 210, 117 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 753, 210, 117 is 3.

Highest Common Factor of 753,210,117 using Euclid's algorithm

Highest Common Factor of 753,210,117 is 3

Step 1: Since 753 > 210, we apply the division lemma to 753 and 210, to get

753 = 210 x 3 + 123

Step 2: Since the reminder 210 ≠ 0, we apply division lemma to 123 and 210, to get

210 = 123 x 1 + 87

Step 3: We consider the new divisor 123 and the new remainder 87, and apply the division lemma to get

123 = 87 x 1 + 36

We consider the new divisor 87 and the new remainder 36,and apply the division lemma to get

87 = 36 x 2 + 15

We consider the new divisor 36 and the new remainder 15,and apply the division lemma to get

36 = 15 x 2 + 6

We consider the new divisor 15 and the new remainder 6,and apply the division lemma to get

15 = 6 x 2 + 3

We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get

6 = 3 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 753 and 210 is 3

Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(36,15) = HCF(87,36) = HCF(123,87) = HCF(210,123) = HCF(753,210) .

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

Step 1: Since 117 > 3, we apply the division lemma to 117 and 3, to get

117 = 3 x 39 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 117 is 3

Notice that 3 = HCF(117,3) .

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Frequently Asked Questions on HCF of 753, 210, 117 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 753, 210, 117?

Answer: HCF of 753, 210, 117 is 3 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 753, 210, 117 using Euclid's Algorithm?

Answer: For arbitrary numbers 753, 210, 117 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.