# Highest Common Factor of 35, 45, 91, 83 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 35, 45, 91, 83 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 35, 45, 91, 83 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 35, 45, 91, 83 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 35, 45, 91, 83 is 1.

HCF(35, 45, 91, 83) = 1

## HCF of 35, 45, 91, 83 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 35, 45, 91, 83 is 1. ### Highest Common Factor of 35,45,91,83 is 1

Step 1: Since 45 > 35, we apply the division lemma to 45 and 35, to get

45 = 35 x 1 + 10

Step 2: Since the reminder 35 ≠ 0, we apply division lemma to 10 and 35, to get

35 = 10 x 3 + 5

Step 3: 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 35 and 45 is 5

Notice that 5 = HCF(10,5) = HCF(35,10) = HCF(45,35) .

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

Step 1: Since 91 > 5, we apply the division lemma to 91 and 5, to get

91 = 5 x 18 + 1

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 1 and 5, to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5 and 91 is 1

Notice that 1 = HCF(5,1) = HCF(91,5) .

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

Step 1: Since 83 > 1, we apply the division lemma to 83 and 1, to get

83 = 1 x 83 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 83 is 1

Notice that 1 = HCF(83,1) .

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### Frequently Asked Questions on HCF of 35, 45, 91, 83 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 35, 45, 91, 83?

Answer: HCF of 35, 45, 91, 83 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 35, 45, 91, 83 using Euclid's Algorithm?

Answer: For arbitrary numbers 35, 45, 91, 83 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.