Highest Common Factor of 608, 968, 160 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 608, 968, 160 i.e. 8 the largest integer that leaves a remainder zero for all numbers.

HCF of 608, 968, 160 is 8 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 608, 968, 160 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 608, 968, 160 is 8.

HCF(608, 968, 160) = 8

HCF of 608, 968, 160 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 608, 968, 160 is 8.

Highest Common Factor of 608,968,160 using Euclid's algorithm

Highest Common Factor of 608,968,160 is 8

Step 1: Since 968 > 608, we apply the division lemma to 968 and 608, to get

968 = 608 x 1 + 360

Step 2: Since the reminder 608 ≠ 0, we apply division lemma to 360 and 608, to get

608 = 360 x 1 + 248

Step 3: We consider the new divisor 360 and the new remainder 248, and apply the division lemma to get

360 = 248 x 1 + 112

We consider the new divisor 248 and the new remainder 112,and apply the division lemma to get

248 = 112 x 2 + 24

We consider the new divisor 112 and the new remainder 24,and apply the division lemma to get

112 = 24 x 4 + 16

We consider the new divisor 24 and the new remainder 16,and apply the division lemma to get

24 = 16 x 1 + 8

We consider the new divisor 16 and the new remainder 8,and apply the division lemma to get

16 = 8 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 608 and 968 is 8

Notice that 8 = HCF(16,8) = HCF(24,16) = HCF(112,24) = HCF(248,112) = HCF(360,248) = HCF(608,360) = HCF(968,608) .

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

Step 1: Since 160 > 8, we apply the division lemma to 160 and 8, to get

160 = 8 x 20 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 8 and 160 is 8

Notice that 8 = HCF(160,8) .

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Frequently Asked Questions on HCF of 608, 968, 160 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 608, 968, 160?

Answer: HCF of 608, 968, 160 is 8 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 608, 968, 160 using Euclid's Algorithm?

Answer: For arbitrary numbers 608, 968, 160 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.