Highest Common Factor of 7692, 5408 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 7692, 5408 i.e. 4 the largest integer that leaves a remainder zero for all numbers.

HCF of 7692, 5408 is 4 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 7692, 5408 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 7692, 5408 is 4.

HCF(7692, 5408) = 4

HCF of 7692, 5408 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 7692, 5408 is 4.

Highest Common Factor of 7692,5408 using Euclid's algorithm

Highest Common Factor of 7692,5408 is 4

Step 1: Since 7692 > 5408, we apply the division lemma to 7692 and 5408, to get

7692 = 5408 x 1 + 2284

Step 2: Since the reminder 5408 ≠ 0, we apply division lemma to 2284 and 5408, to get

5408 = 2284 x 2 + 840

Step 3: We consider the new divisor 2284 and the new remainder 840, and apply the division lemma to get

2284 = 840 x 2 + 604

We consider the new divisor 840 and the new remainder 604,and apply the division lemma to get

840 = 604 x 1 + 236

We consider the new divisor 604 and the new remainder 236,and apply the division lemma to get

604 = 236 x 2 + 132

We consider the new divisor 236 and the new remainder 132,and apply the division lemma to get

236 = 132 x 1 + 104

We consider the new divisor 132 and the new remainder 104,and apply the division lemma to get

132 = 104 x 1 + 28

We consider the new divisor 104 and the new remainder 28,and apply the division lemma to get

104 = 28 x 3 + 20

We consider the new divisor 28 and the new remainder 20,and apply the division lemma to get

28 = 20 x 1 + 8

We consider the new divisor 20 and the new remainder 8,and apply the division lemma to get

20 = 8 x 2 + 4

We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get

8 = 4 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 7692 and 5408 is 4

Notice that 4 = HCF(8,4) = HCF(20,8) = HCF(28,20) = HCF(104,28) = HCF(132,104) = HCF(236,132) = HCF(604,236) = HCF(840,604) = HCF(2284,840) = HCF(5408,2284) = HCF(7692,5408) .

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Frequently Asked Questions on HCF of 7692, 5408 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 7692, 5408?

Answer: HCF of 7692, 5408 is 4 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 7692, 5408 using Euclid's Algorithm?

Answer: For arbitrary numbers 7692, 5408 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.