Highest Common Factor of 748, 295, 601 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 748, 295, 601 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 748, 295, 601 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 748, 295, 601 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 748, 295, 601 is 1.

HCF(748, 295, 601) = 1

HCF of 748, 295, 601 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 748, 295, 601 is 1.

Highest Common Factor of 748,295,601 using Euclid's algorithm

Highest Common Factor of 748,295,601 is 1

Step 1: Since 748 > 295, we apply the division lemma to 748 and 295, to get

748 = 295 x 2 + 158

Step 2: Since the reminder 295 ≠ 0, we apply division lemma to 158 and 295, to get

295 = 158 x 1 + 137

Step 3: We consider the new divisor 158 and the new remainder 137, and apply the division lemma to get

158 = 137 x 1 + 21

We consider the new divisor 137 and the new remainder 21,and apply the division lemma to get

137 = 21 x 6 + 11

We consider the new divisor 21 and the new remainder 11,and apply the division lemma to get

21 = 11 x 1 + 10

We consider the new divisor 11 and the new remainder 10,and apply the division lemma to get

11 = 10 x 1 + 1

We consider the new divisor 10 and the new remainder 1,and apply the division lemma to get

10 = 1 x 10 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 748 and 295 is 1

Notice that 1 = HCF(10,1) = HCF(11,10) = HCF(21,11) = HCF(137,21) = HCF(158,137) = HCF(295,158) = HCF(748,295) .

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

Step 1: Since 601 > 1, we apply the division lemma to 601 and 1, to get

601 = 1 x 601 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 601 is 1

Notice that 1 = HCF(601,1) .

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Frequently Asked Questions on HCF of 748, 295, 601 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 748, 295, 601?

Answer: HCF of 748, 295, 601 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 748, 295, 601 using Euclid's Algorithm?

Answer: For arbitrary numbers 748, 295, 601 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.