Highest Common Factor of 374, 975 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 374, 975 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 374, 975 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 374, 975 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 374, 975 is 1.

HCF(374, 975) = 1

HCF of 374, 975 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 374, 975 is 1.

Highest Common Factor of 374,975 using Euclid's algorithm

Highest Common Factor of 374,975 is 1

Step 1: Since 975 > 374, we apply the division lemma to 975 and 374, to get

975 = 374 x 2 + 227

Step 2: Since the reminder 374 ≠ 0, we apply division lemma to 227 and 374, to get

374 = 227 x 1 + 147

Step 3: We consider the new divisor 227 and the new remainder 147, and apply the division lemma to get

227 = 147 x 1 + 80

We consider the new divisor 147 and the new remainder 80,and apply the division lemma to get

147 = 80 x 1 + 67

We consider the new divisor 80 and the new remainder 67,and apply the division lemma to get

80 = 67 x 1 + 13

We consider the new divisor 67 and the new remainder 13,and apply the division lemma to get

67 = 13 x 5 + 2

We consider the new divisor 13 and the new remainder 2,and apply the division lemma to get

13 = 2 x 6 + 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 374 and 975 is 1

Notice that 1 = HCF(2,1) = HCF(13,2) = HCF(67,13) = HCF(80,67) = HCF(147,80) = HCF(227,147) = HCF(374,227) = HCF(975,374) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 374, 975 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 374, 975?

Answer: HCF of 374, 975 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 374, 975 using Euclid's Algorithm?

Answer: For arbitrary numbers 374, 975 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.