Highest Common Factor of 969, 409 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 969, 409 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 969, 409 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 969, 409 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 969, 409 is 1.

HCF(969, 409) = 1

HCF of 969, 409 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 969, 409 is 1.

Highest Common Factor of 969,409 using Euclid's algorithm

Highest Common Factor of 969,409 is 1

Step 1: Since 969 > 409, we apply the division lemma to 969 and 409, to get

969 = 409 x 2 + 151

Step 2: Since the reminder 409 ≠ 0, we apply division lemma to 151 and 409, to get

409 = 151 x 2 + 107

Step 3: We consider the new divisor 151 and the new remainder 107, and apply the division lemma to get

151 = 107 x 1 + 44

We consider the new divisor 107 and the new remainder 44,and apply the division lemma to get

107 = 44 x 2 + 19

We consider the new divisor 44 and the new remainder 19,and apply the division lemma to get

44 = 19 x 2 + 6

We consider the new divisor 19 and the new remainder 6,and apply the division lemma to get

19 = 6 x 3 + 1

We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get

6 = 1 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 969 and 409 is 1

Notice that 1 = HCF(6,1) = HCF(19,6) = HCF(44,19) = HCF(107,44) = HCF(151,107) = HCF(409,151) = HCF(969,409) .

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Frequently Asked Questions on HCF of 969, 409 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 969, 409?

Answer: HCF of 969, 409 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 969, 409 using Euclid's Algorithm?

Answer: For arbitrary numbers 969, 409 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.