Highest Common Factor of 407, 480, 996 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 407, 480, 996 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 407, 480, 996 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 407, 480, 996 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 407, 480, 996 is 1.

HCF(407, 480, 996) = 1

HCF of 407, 480, 996 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 407, 480, 996 is 1.

Highest Common Factor of 407,480,996 using Euclid's algorithm

Highest Common Factor of 407,480,996 is 1

Step 1: Since 480 > 407, we apply the division lemma to 480 and 407, to get

480 = 407 x 1 + 73

Step 2: Since the reminder 407 ≠ 0, we apply division lemma to 73 and 407, to get

407 = 73 x 5 + 42

Step 3: We consider the new divisor 73 and the new remainder 42, and apply the division lemma to get

73 = 42 x 1 + 31

We consider the new divisor 42 and the new remainder 31,and apply the division lemma to get

42 = 31 x 1 + 11

We consider the new divisor 31 and the new remainder 11,and apply the division lemma to get

31 = 11 x 2 + 9

We consider the new divisor 11 and the new remainder 9,and apply the division lemma to get

11 = 9 x 1 + 2

We consider the new divisor 9 and the new remainder 2,and apply the division lemma to get

9 = 2 x 4 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 407 and 480 is 1

Notice that 1 = HCF(2,1) = HCF(9,2) = HCF(11,9) = HCF(31,11) = HCF(42,31) = HCF(73,42) = HCF(407,73) = HCF(480,407) .

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

Step 1: Since 996 > 1, we apply the division lemma to 996 and 1, to get

996 = 1 x 996 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 996 is 1

Notice that 1 = HCF(996,1) .

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Frequently Asked Questions on HCF of 407, 480, 996 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 407, 480, 996?

Answer: HCF of 407, 480, 996 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 407, 480, 996 using Euclid's Algorithm?

Answer: For arbitrary numbers 407, 480, 996 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.