Highest Common Factor of 46, 66, 969, 401 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 46, 66, 969, 401 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 46, 66, 969, 401 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 46, 66, 969, 401 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 46, 66, 969, 401 is 1.

HCF(46, 66, 969, 401) = 1

HCF of 46, 66, 969, 401 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 46, 66, 969, 401 is 1.

Highest Common Factor of 46,66,969,401 using Euclid's algorithm

Highest Common Factor of 46,66,969,401 is 1

Step 1: Since 66 > 46, we apply the division lemma to 66 and 46, to get

66 = 46 x 1 + 20

Step 2: Since the reminder 46 ≠ 0, we apply division lemma to 20 and 46, to get

46 = 20 x 2 + 6

Step 3: We consider the new divisor 20 and the new remainder 6, and apply the division lemma to get

20 = 6 x 3 + 2

We consider the new divisor 6 and the new remainder 2, and apply the division lemma to get

6 = 2 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 46 and 66 is 2

Notice that 2 = HCF(6,2) = HCF(20,6) = HCF(46,20) = HCF(66,46) .

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

Step 1: Since 969 > 2, we apply the division lemma to 969 and 2, to get

969 = 2 x 484 + 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 969 is 1

Notice that 1 = HCF(2,1) = HCF(969,2) .

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

Step 1: Since 401 > 1, we apply the division lemma to 401 and 1, to get

401 = 1 x 401 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 401 is 1

Notice that 1 = HCF(401,1) .

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Frequently Asked Questions on HCF of 46, 66, 969, 401 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 46, 66, 969, 401?

Answer: HCF of 46, 66, 969, 401 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 46, 66, 969, 401 using Euclid's Algorithm?

Answer: For arbitrary numbers 46, 66, 969, 401 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.