Highest Common Factor of 975, 805, 223 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 975, 805, 223 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 975, 805, 223 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 975, 805, 223 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 975, 805, 223 is 1.

HCF(975, 805, 223) = 1

HCF of 975, 805, 223 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 975, 805, 223 is 1.

Highest Common Factor of 975,805,223 using Euclid's algorithm

Highest Common Factor of 975,805,223 is 1

Step 1: Since 975 > 805, we apply the division lemma to 975 and 805, to get

975 = 805 x 1 + 170

Step 2: Since the reminder 805 ≠ 0, we apply division lemma to 170 and 805, to get

805 = 170 x 4 + 125

Step 3: We consider the new divisor 170 and the new remainder 125, and apply the division lemma to get

170 = 125 x 1 + 45

We consider the new divisor 125 and the new remainder 45,and apply the division lemma to get

125 = 45 x 2 + 35

We consider the new divisor 45 and the new remainder 35,and apply the division lemma to get

45 = 35 x 1 + 10

We consider the new divisor 35 and the new remainder 10,and apply the division lemma to get

35 = 10 x 3 + 5

We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get

10 = 5 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 975 and 805 is 5

Notice that 5 = HCF(10,5) = HCF(35,10) = HCF(45,35) = HCF(125,45) = HCF(170,125) = HCF(805,170) = HCF(975,805) .

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

Step 1: Since 223 > 5, we apply the division lemma to 223 and 5, to get

223 = 5 x 44 + 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 223 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(223,5) .

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Frequently Asked Questions on HCF of 975, 805, 223 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 975, 805, 223?

Answer: HCF of 975, 805, 223 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 975, 805, 223 using Euclid's Algorithm?

Answer: For arbitrary numbers 975, 805, 223 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.