Highest Common Factor of 640, 714, 352, 575 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 640, 714, 352, 575 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 640, 714, 352, 575 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 640, 714, 352, 575 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 640, 714, 352, 575 is 1.

HCF(640, 714, 352, 575) = 1

HCF of 640, 714, 352, 575 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 640, 714, 352, 575 is 1.

Highest Common Factor of 640,714,352,575 using Euclid's algorithm

Highest Common Factor of 640,714,352,575 is 1

Step 1: Since 714 > 640, we apply the division lemma to 714 and 640, to get

714 = 640 x 1 + 74

Step 2: Since the reminder 640 ≠ 0, we apply division lemma to 74 and 640, to get

640 = 74 x 8 + 48

Step 3: We consider the new divisor 74 and the new remainder 48, and apply the division lemma to get

74 = 48 x 1 + 26

We consider the new divisor 48 and the new remainder 26,and apply the division lemma to get

48 = 26 x 1 + 22

We consider the new divisor 26 and the new remainder 22,and apply the division lemma to get

26 = 22 x 1 + 4

We consider the new divisor 22 and the new remainder 4,and apply the division lemma to get

22 = 4 x 5 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 640 and 714 is 2

Notice that 2 = HCF(4,2) = HCF(22,4) = HCF(26,22) = HCF(48,26) = HCF(74,48) = HCF(640,74) = HCF(714,640) .

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

Step 1: Since 352 > 2, we apply the division lemma to 352 and 2, to get

352 = 2 x 176 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 352 is 2

Notice that 2 = HCF(352,2) .

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

Step 1: Since 575 > 2, we apply the division lemma to 575 and 2, to get

575 = 2 x 287 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 575 is 1

Notice that 1 = HCF(2,1) = HCF(575,2) .

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Frequently Asked Questions on HCF of 640, 714, 352, 575 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 640, 714, 352, 575?

Answer: HCF of 640, 714, 352, 575 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 640, 714, 352, 575 using Euclid's Algorithm?

Answer: For arbitrary numbers 640, 714, 352, 575 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.