Highest Common Factor of 635, 975, 32 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 635, 975, 32 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 635, 975, 32 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 635, 975, 32 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 635, 975, 32 is 1.

HCF(635, 975, 32) = 1

HCF of 635, 975, 32 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 635, 975, 32 is 1.

Highest Common Factor of 635,975,32 using Euclid's algorithm

Highest Common Factor of 635,975,32 is 1

Step 1: Since 975 > 635, we apply the division lemma to 975 and 635, to get

975 = 635 x 1 + 340

Step 2: Since the reminder 635 ≠ 0, we apply division lemma to 340 and 635, to get

635 = 340 x 1 + 295

Step 3: We consider the new divisor 340 and the new remainder 295, and apply the division lemma to get

340 = 295 x 1 + 45

We consider the new divisor 295 and the new remainder 45,and apply the division lemma to get

295 = 45 x 6 + 25

We consider the new divisor 45 and the new remainder 25,and apply the division lemma to get

45 = 25 x 1 + 20

We consider the new divisor 25 and the new remainder 20,and apply the division lemma to get

25 = 20 x 1 + 5

We consider the new divisor 20 and the new remainder 5,and apply the division lemma to get

20 = 5 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 635 and 975 is 5

Notice that 5 = HCF(20,5) = HCF(25,20) = HCF(45,25) = HCF(295,45) = HCF(340,295) = HCF(635,340) = HCF(975,635) .

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

Step 1: Since 32 > 5, we apply the division lemma to 32 and 5, to get

32 = 5 x 6 + 2

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

5 = 2 x 2 + 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 5 and 32 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(32,5) .

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Frequently Asked Questions on HCF of 635, 975, 32 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 635, 975, 32?

Answer: HCF of 635, 975, 32 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 635, 975, 32 using Euclid's Algorithm?

Answer: For arbitrary numbers 635, 975, 32 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.