Highest Common Factor of 968, 1562, 3407 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 968, 1562, 3407 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 968, 1562, 3407 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 968, 1562, 3407 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 968, 1562, 3407 is 1.

HCF(968, 1562, 3407) = 1

HCF of 968, 1562, 3407 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 968, 1562, 3407 is 1.

Highest Common Factor of 968,1562,3407 using Euclid's algorithm

Highest Common Factor of 968,1562,3407 is 1

Step 1: Since 1562 > 968, we apply the division lemma to 1562 and 968, to get

1562 = 968 x 1 + 594

Step 2: Since the reminder 968 ≠ 0, we apply division lemma to 594 and 968, to get

968 = 594 x 1 + 374

Step 3: We consider the new divisor 594 and the new remainder 374, and apply the division lemma to get

594 = 374 x 1 + 220

We consider the new divisor 374 and the new remainder 220,and apply the division lemma to get

374 = 220 x 1 + 154

We consider the new divisor 220 and the new remainder 154,and apply the division lemma to get

220 = 154 x 1 + 66

We consider the new divisor 154 and the new remainder 66,and apply the division lemma to get

154 = 66 x 2 + 22

We consider the new divisor 66 and the new remainder 22,and apply the division lemma to get

66 = 22 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 22, the HCF of 968 and 1562 is 22

Notice that 22 = HCF(66,22) = HCF(154,66) = HCF(220,154) = HCF(374,220) = HCF(594,374) = HCF(968,594) = HCF(1562,968) .

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

Step 1: Since 3407 > 22, we apply the division lemma to 3407 and 22, to get

3407 = 22 x 154 + 19

Step 2: Since the reminder 22 ≠ 0, we apply division lemma to 19 and 22, to get

22 = 19 x 1 + 3

Step 3: We consider the new divisor 19 and the new remainder 3, and apply the division lemma to get

19 = 3 x 6 + 1

We consider the new divisor 3 and the new remainder 1, and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 22 and 3407 is 1

Notice that 1 = HCF(3,1) = HCF(19,3) = HCF(22,19) = HCF(3407,22) .

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Frequently Asked Questions on HCF of 968, 1562, 3407 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 968, 1562, 3407?

Answer: HCF of 968, 1562, 3407 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 968, 1562, 3407 using Euclid's Algorithm?

Answer: For arbitrary numbers 968, 1562, 3407 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.