Highest Common Factor of 640, 865, 668, 358 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, 865, 668, 358 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 640, 865, 668, 358 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, 865, 668, 358 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, 865, 668, 358 is 1.

HCF(640, 865, 668, 358) = 1

HCF of 640, 865, 668, 358 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, 865, 668, 358 is 1.

Highest Common Factor of 640,865,668,358 using Euclid's algorithm

Highest Common Factor of 640,865,668,358 is 1

Step 1: Since 865 > 640, we apply the division lemma to 865 and 640, to get

865 = 640 x 1 + 225

Step 2: Since the reminder 640 ≠ 0, we apply division lemma to 225 and 640, to get

640 = 225 x 2 + 190

Step 3: We consider the new divisor 225 and the new remainder 190, and apply the division lemma to get

225 = 190 x 1 + 35

We consider the new divisor 190 and the new remainder 35,and apply the division lemma to get

190 = 35 x 5 + 15

We consider the new divisor 35 and the new remainder 15,and apply the division lemma to get

35 = 15 x 2 + 5

We consider the new divisor 15 and the new remainder 5,and apply the division lemma to get

15 = 5 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 640 and 865 is 5

Notice that 5 = HCF(15,5) = HCF(35,15) = HCF(190,35) = HCF(225,190) = HCF(640,225) = HCF(865,640) .

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

Step 1: Since 668 > 5, we apply the division lemma to 668 and 5, to get

668 = 5 x 133 + 3

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 3 and 5, to get

5 = 3 x 1 + 2

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

3 = 2 x 1 + 1

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 5 and 668 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(668,5) .

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

Step 1: Since 358 > 1, we apply the division lemma to 358 and 1, to get

358 = 1 x 358 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 358 is 1

Notice that 1 = HCF(358,1) .

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Frequently Asked Questions on HCF of 640, 865, 668, 358 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, 865, 668, 358?

Answer: HCF of 640, 865, 668, 358 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 640, 865, 668, 358 using Euclid's Algorithm?

Answer: For arbitrary numbers 640, 865, 668, 358 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.