Highest Common Factor of 122, 440, 512, 121 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 122, 440, 512, 121 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 122, 440, 512, 121 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 122, 440, 512, 121 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 122, 440, 512, 121 is 1.

HCF(122, 440, 512, 121) = 1

HCF of 122, 440, 512, 121 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 122, 440, 512, 121 is 1.

Highest Common Factor of 122,440,512,121 using Euclid's algorithm

Highest Common Factor of 122,440,512,121 is 1

Step 1: Since 440 > 122, we apply the division lemma to 440 and 122, to get

440 = 122 x 3 + 74

Step 2: Since the reminder 122 ≠ 0, we apply division lemma to 74 and 122, to get

122 = 74 x 1 + 48

Step 3: We consider the new divisor 74 and the new remainder 48, and apply the division lemma to get

74 = 48 x 1 + 26

We consider the new divisor 48 and the new remainder 26,and apply the division lemma to get

48 = 26 x 1 + 22

We consider the new divisor 26 and the new remainder 22,and apply the division lemma to get

26 = 22 x 1 + 4

We consider the new divisor 22 and the new remainder 4,and apply the division lemma to get

22 = 4 x 5 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 122 and 440 is 2

Notice that 2 = HCF(4,2) = HCF(22,4) = HCF(26,22) = HCF(48,26) = HCF(74,48) = HCF(122,74) = HCF(440,122) .

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

Step 1: Since 512 > 2, we apply the division lemma to 512 and 2, to get

512 = 2 x 256 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 512 is 2

Notice that 2 = HCF(512,2) .

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

Step 1: Since 121 > 2, we apply the division lemma to 121 and 2, to get

121 = 2 x 60 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 121 is 1

Notice that 1 = HCF(2,1) = HCF(121,2) .

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Frequently Asked Questions on HCF of 122, 440, 512, 121 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 122, 440, 512, 121?

Answer: HCF of 122, 440, 512, 121 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 122, 440, 512, 121 using Euclid's Algorithm?

Answer: For arbitrary numbers 122, 440, 512, 121 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.