Highest Common Factor of 74, 87, 96, 84 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 74, 87, 96, 84 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 74, 87, 96, 84 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 74, 87, 96, 84 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 74, 87, 96, 84 is 1.

HCF(74, 87, 96, 84) = 1

HCF of 74, 87, 96, 84 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 74, 87, 96, 84 is 1.

Highest Common Factor of 74,87,96,84 using Euclid's algorithm

Highest Common Factor of 74,87,96,84 is 1

Step 1: Since 87 > 74, we apply the division lemma to 87 and 74, to get

87 = 74 x 1 + 13

Step 2: Since the reminder 74 ≠ 0, we apply division lemma to 13 and 74, to get

74 = 13 x 5 + 9

Step 3: We consider the new divisor 13 and the new remainder 9, and apply the division lemma to get

13 = 9 x 1 + 4

We consider the new divisor 9 and the new remainder 4,and apply the division lemma to get

9 = 4 x 2 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 74 and 87 is 1

Notice that 1 = HCF(4,1) = HCF(9,4) = HCF(13,9) = HCF(74,13) = HCF(87,74) .

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

Step 1: Since 96 > 1, we apply the division lemma to 96 and 1, to get

96 = 1 x 96 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 96 is 1

Notice that 1 = HCF(96,1) .

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

Step 1: Since 84 > 1, we apply the division lemma to 84 and 1, to get

84 = 1 x 84 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 84 is 1

Notice that 1 = HCF(84,1) .

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Frequently Asked Questions on HCF of 74, 87, 96, 84 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 74, 87, 96, 84?

Answer: HCF of 74, 87, 96, 84 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 74, 87, 96, 84 using Euclid's Algorithm?

Answer: For arbitrary numbers 74, 87, 96, 84 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.