Highest Common Factor of 417, 561, 374 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 417, 561, 374 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 417, 561, 374 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 417, 561, 374 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 417, 561, 374 is 1.

HCF(417, 561, 374) = 1

HCF of 417, 561, 374 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 417, 561, 374 is 1.

Highest Common Factor of 417,561,374 using Euclid's algorithm

Highest Common Factor of 417,561,374 is 1

Step 1: Since 561 > 417, we apply the division lemma to 561 and 417, to get

561 = 417 x 1 + 144

Step 2: Since the reminder 417 ≠ 0, we apply division lemma to 144 and 417, to get

417 = 144 x 2 + 129

Step 3: We consider the new divisor 144 and the new remainder 129, and apply the division lemma to get

144 = 129 x 1 + 15

We consider the new divisor 129 and the new remainder 15,and apply the division lemma to get

129 = 15 x 8 + 9

We consider the new divisor 15 and the new remainder 9,and apply the division lemma to get

15 = 9 x 1 + 6

We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get

9 = 6 x 1 + 3

We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get

6 = 3 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 417 and 561 is 3

Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(15,9) = HCF(129,15) = HCF(144,129) = HCF(417,144) = HCF(561,417) .

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

Step 1: Since 374 > 3, we apply the division lemma to 374 and 3, to get

374 = 3 x 124 + 2

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get

3 = 2 x 1 + 1

Step 3: 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 3 and 374 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(374,3) .

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Frequently Asked Questions on HCF of 417, 561, 374 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 417, 561, 374?

Answer: HCF of 417, 561, 374 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 417, 561, 374 using Euclid's Algorithm?

Answer: For arbitrary numbers 417, 561, 374 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.