Highest Common Factor of 352, 560, 398 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 352, 560, 398 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 352, 560, 398 is 2 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 352, 560, 398 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 352, 560, 398 is 2.

HCF(352, 560, 398) = 2

HCF of 352, 560, 398 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 352, 560, 398 is 2.

Highest Common Factor of 352,560,398 using Euclid's algorithm

Highest Common Factor of 352,560,398 is 2

Step 1: Since 560 > 352, we apply the division lemma to 560 and 352, to get

560 = 352 x 1 + 208

Step 2: Since the reminder 352 ≠ 0, we apply division lemma to 208 and 352, to get

352 = 208 x 1 + 144

Step 3: We consider the new divisor 208 and the new remainder 144, and apply the division lemma to get

208 = 144 x 1 + 64

We consider the new divisor 144 and the new remainder 64,and apply the division lemma to get

144 = 64 x 2 + 16

We consider the new divisor 64 and the new remainder 16,and apply the division lemma to get

64 = 16 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 16, the HCF of 352 and 560 is 16

Notice that 16 = HCF(64,16) = HCF(144,64) = HCF(208,144) = HCF(352,208) = HCF(560,352) .


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

Step 1: Since 398 > 16, we apply the division lemma to 398 and 16, to get

398 = 16 x 24 + 14

Step 2: Since the reminder 16 ≠ 0, we apply division lemma to 14 and 16, to get

16 = 14 x 1 + 2

Step 3: We consider the new divisor 14 and the new remainder 2, and apply the division lemma to get

14 = 2 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 16 and 398 is 2

Notice that 2 = HCF(14,2) = HCF(16,14) = HCF(398,16) .

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Frequently Asked Questions on HCF of 352, 560, 398 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 352, 560, 398?

Answer: HCF of 352, 560, 398 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 352, 560, 398 using Euclid's Algorithm?

Answer: For arbitrary numbers 352, 560, 398 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.