Highest Common Factor of 975, 769, 448 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, 769, 448 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 975, 769, 448 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, 769, 448 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, 769, 448 is 1.

HCF(975, 769, 448) = 1

HCF of 975, 769, 448 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, 769, 448 is 1.

Highest Common Factor of 975,769,448 using Euclid's algorithm

Highest Common Factor of 975,769,448 is 1

Step 1: Since 975 > 769, we apply the division lemma to 975 and 769, to get

975 = 769 x 1 + 206

Step 2: Since the reminder 769 ≠ 0, we apply division lemma to 206 and 769, to get

769 = 206 x 3 + 151

Step 3: We consider the new divisor 206 and the new remainder 151, and apply the division lemma to get

206 = 151 x 1 + 55

We consider the new divisor 151 and the new remainder 55,and apply the division lemma to get

151 = 55 x 2 + 41

We consider the new divisor 55 and the new remainder 41,and apply the division lemma to get

55 = 41 x 1 + 14

We consider the new divisor 41 and the new remainder 14,and apply the division lemma to get

41 = 14 x 2 + 13

We consider the new divisor 14 and the new remainder 13,and apply the division lemma to get

14 = 13 x 1 + 1

We consider the new divisor 13 and the new remainder 1,and apply the division lemma to get

13 = 1 x 13 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 975 and 769 is 1

Notice that 1 = HCF(13,1) = HCF(14,13) = HCF(41,14) = HCF(55,41) = HCF(151,55) = HCF(206,151) = HCF(769,206) = HCF(975,769) .

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

Step 1: Since 448 > 1, we apply the division lemma to 448 and 1, to get

448 = 1 x 448 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 448 is 1

Notice that 1 = HCF(448,1) .

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Frequently Asked Questions on HCF of 975, 769, 448 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, 769, 448?

Answer: HCF of 975, 769, 448 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 975, 769, 448 using Euclid's Algorithm?

Answer: For arbitrary numbers 975, 769, 448 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.