Highest Common Factor of 120, 991, 275 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 120, 991, 275 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 120, 991, 275 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 120, 991, 275 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 120, 991, 275 is 1.

HCF(120, 991, 275) = 1

HCF of 120, 991, 275 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 120, 991, 275 is 1.

Highest Common Factor of 120,991,275 using Euclid's algorithm

Highest Common Factor of 120,991,275 is 1

Step 1: Since 991 > 120, we apply the division lemma to 991 and 120, to get

991 = 120 x 8 + 31

Step 2: Since the reminder 120 ≠ 0, we apply division lemma to 31 and 120, to get

120 = 31 x 3 + 27

Step 3: We consider the new divisor 31 and the new remainder 27, and apply the division lemma to get

31 = 27 x 1 + 4

We consider the new divisor 27 and the new remainder 4,and apply the division lemma to get

27 = 4 x 6 + 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 120 and 991 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(27,4) = HCF(31,27) = HCF(120,31) = HCF(991,120) .

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

Step 1: Since 275 > 1, we apply the division lemma to 275 and 1, to get

275 = 1 x 275 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 275 is 1

Notice that 1 = HCF(275,1) .

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Frequently Asked Questions on HCF of 120, 991, 275 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 120, 991, 275?

Answer: HCF of 120, 991, 275 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 120, 991, 275 using Euclid's Algorithm?

Answer: For arbitrary numbers 120, 991, 275 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.