Highest Common Factor of 235, 372, 350 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 235, 372, 350 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 235, 372, 350 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 235, 372, 350 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 235, 372, 350 is 1.

HCF(235, 372, 350) = 1

HCF of 235, 372, 350 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 235, 372, 350 is 1.

Highest Common Factor of 235,372,350 using Euclid's algorithm

Highest Common Factor of 235,372,350 is 1

Step 1: Since 372 > 235, we apply the division lemma to 372 and 235, to get

372 = 235 x 1 + 137

Step 2: Since the reminder 235 ≠ 0, we apply division lemma to 137 and 235, to get

235 = 137 x 1 + 98

Step 3: We consider the new divisor 137 and the new remainder 98, and apply the division lemma to get

137 = 98 x 1 + 39

We consider the new divisor 98 and the new remainder 39,and apply the division lemma to get

98 = 39 x 2 + 20

We consider the new divisor 39 and the new remainder 20,and apply the division lemma to get

39 = 20 x 1 + 19

We consider the new divisor 20 and the new remainder 19,and apply the division lemma to get

20 = 19 x 1 + 1

We consider the new divisor 19 and the new remainder 1,and apply the division lemma to get

19 = 1 x 19 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 235 and 372 is 1

Notice that 1 = HCF(19,1) = HCF(20,19) = HCF(39,20) = HCF(98,39) = HCF(137,98) = HCF(235,137) = HCF(372,235) .

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

Step 1: Since 350 > 1, we apply the division lemma to 350 and 1, to get

350 = 1 x 350 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 350 is 1

Notice that 1 = HCF(350,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 235, 372, 350 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 235, 372, 350?

Answer: HCF of 235, 372, 350 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 235, 372, 350 using Euclid's Algorithm?

Answer: For arbitrary numbers 235, 372, 350 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.