Highest Common Factor of 965, 856, 122 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 965, 856, 122 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 965, 856, 122 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 965, 856, 122 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 965, 856, 122 is 1.

HCF(965, 856, 122) = 1

HCF of 965, 856, 122 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 965, 856, 122 is 1.

Highest Common Factor of 965,856,122 using Euclid's algorithm

Highest Common Factor of 965,856,122 is 1

Step 1: Since 965 > 856, we apply the division lemma to 965 and 856, to get

965 = 856 x 1 + 109

Step 2: Since the reminder 856 ≠ 0, we apply division lemma to 109 and 856, to get

856 = 109 x 7 + 93

Step 3: We consider the new divisor 109 and the new remainder 93, and apply the division lemma to get

109 = 93 x 1 + 16

We consider the new divisor 93 and the new remainder 16,and apply the division lemma to get

93 = 16 x 5 + 13

We consider the new divisor 16 and the new remainder 13,and apply the division lemma to get

16 = 13 x 1 + 3

We consider the new divisor 13 and the new remainder 3,and apply the division lemma to get

13 = 3 x 4 + 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 965 and 856 is 1

Notice that 1 = HCF(3,1) = HCF(13,3) = HCF(16,13) = HCF(93,16) = HCF(109,93) = HCF(856,109) = HCF(965,856) .

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

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

122 = 1 x 122 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 122 is 1

Notice that 1 = HCF(122,1) .

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Frequently Asked Questions on HCF of 965, 856, 122 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 965, 856, 122?

Answer: HCF of 965, 856, 122 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 965, 856, 122 using Euclid's Algorithm?

Answer: For arbitrary numbers 965, 856, 122 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.