Highest Common Factor of 735, 890, 889 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 735, 890, 889 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 735, 890, 889 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 735, 890, 889 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 735, 890, 889 is 1.

HCF(735, 890, 889) = 1

HCF of 735, 890, 889 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 735, 890, 889 is 1.

Highest Common Factor of 735,890,889 using Euclid's algorithm

Highest Common Factor of 735,890,889 is 1

Step 1: Since 890 > 735, we apply the division lemma to 890 and 735, to get

890 = 735 x 1 + 155

Step 2: Since the reminder 735 ≠ 0, we apply division lemma to 155 and 735, to get

735 = 155 x 4 + 115

Step 3: We consider the new divisor 155 and the new remainder 115, and apply the division lemma to get

155 = 115 x 1 + 40

We consider the new divisor 115 and the new remainder 40,and apply the division lemma to get

115 = 40 x 2 + 35

We consider the new divisor 40 and the new remainder 35,and apply the division lemma to get

40 = 35 x 1 + 5

We consider the new divisor 35 and the new remainder 5,and apply the division lemma to get

35 = 5 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 735 and 890 is 5

Notice that 5 = HCF(35,5) = HCF(40,35) = HCF(115,40) = HCF(155,115) = HCF(735,155) = HCF(890,735) .

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

Step 1: Since 889 > 5, we apply the division lemma to 889 and 5, to get

889 = 5 x 177 + 4

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 4 and 5, to get

5 = 4 x 1 + 1

Step 3: We consider the new divisor 4 and the new remainder 1, and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5 and 889 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(889,5) .

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Frequently Asked Questions on HCF of 735, 890, 889 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 735, 890, 889?

Answer: HCF of 735, 890, 889 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 735, 890, 889 using Euclid's Algorithm?

Answer: For arbitrary numbers 735, 890, 889 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.