Highest Common Factor of 840, 370, 651 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 840, 370, 651 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 840, 370, 651 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 840, 370, 651 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 840, 370, 651 is 1.

HCF(840, 370, 651) = 1

HCF of 840, 370, 651 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 840, 370, 651 is 1.

Highest Common Factor of 840,370,651 using Euclid's algorithm

Highest Common Factor of 840,370,651 is 1

Step 1: Since 840 > 370, we apply the division lemma to 840 and 370, to get

840 = 370 x 2 + 100

Step 2: Since the reminder 370 ≠ 0, we apply division lemma to 100 and 370, to get

370 = 100 x 3 + 70

Step 3: We consider the new divisor 100 and the new remainder 70, and apply the division lemma to get

100 = 70 x 1 + 30

We consider the new divisor 70 and the new remainder 30,and apply the division lemma to get

70 = 30 x 2 + 10

We consider the new divisor 30 and the new remainder 10,and apply the division lemma to get

30 = 10 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 840 and 370 is 10

Notice that 10 = HCF(30,10) = HCF(70,30) = HCF(100,70) = HCF(370,100) = HCF(840,370) .

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

Step 1: Since 651 > 10, we apply the division lemma to 651 and 10, to get

651 = 10 x 65 + 1

Step 2: Since the reminder 10 ≠ 0, we apply division lemma to 1 and 10, to get

10 = 1 x 10 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 10 and 651 is 1

Notice that 1 = HCF(10,1) = HCF(651,10) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 840, 370, 651 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 840, 370, 651?

Answer: HCF of 840, 370, 651 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 840, 370, 651 using Euclid's Algorithm?

Answer: For arbitrary numbers 840, 370, 651 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.