Highest Common Factor of 980, 775, 735 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 980, 775, 735 i.e. 5 the largest integer that leaves a remainder zero for all numbers.

HCF of 980, 775, 735 is 5 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 980, 775, 735 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 980, 775, 735 is 5.

HCF(980, 775, 735) = 5

HCF of 980, 775, 735 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 980, 775, 735 is 5.

Highest Common Factor of 980,775,735 using Euclid's algorithm

Highest Common Factor of 980,775,735 is 5

Step 1: Since 980 > 775, we apply the division lemma to 980 and 775, to get

980 = 775 x 1 + 205

Step 2: Since the reminder 775 ≠ 0, we apply division lemma to 205 and 775, to get

775 = 205 x 3 + 160

Step 3: We consider the new divisor 205 and the new remainder 160, and apply the division lemma to get

205 = 160 x 1 + 45

We consider the new divisor 160 and the new remainder 45,and apply the division lemma to get

160 = 45 x 3 + 25

We consider the new divisor 45 and the new remainder 25,and apply the division lemma to get

45 = 25 x 1 + 20

We consider the new divisor 25 and the new remainder 20,and apply the division lemma to get

25 = 20 x 1 + 5

We consider the new divisor 20 and the new remainder 5,and apply the division lemma to get

20 = 5 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 980 and 775 is 5

Notice that 5 = HCF(20,5) = HCF(25,20) = HCF(45,25) = HCF(160,45) = HCF(205,160) = HCF(775,205) = HCF(980,775) .

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

Step 1: Since 735 > 5, we apply the division lemma to 735 and 5, to get

735 = 5 x 147 + 0

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

Notice that 5 = HCF(735,5) .

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Frequently Asked Questions on HCF of 980, 775, 735 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 980, 775, 735?

Answer: HCF of 980, 775, 735 is 5 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 980, 775, 735 using Euclid's Algorithm?

Answer: For arbitrary numbers 980, 775, 735 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.