Highest Common Factor of 830, 235, 74, 132 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 830, 235, 74, 132 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 830, 235, 74, 132 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 830, 235, 74, 132 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 830, 235, 74, 132 is 1.

HCF(830, 235, 74, 132) = 1

HCF of 830, 235, 74, 132 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 830, 235, 74, 132 is 1.

Highest Common Factor of 830,235,74,132 using Euclid's algorithm

Highest Common Factor of 830,235,74,132 is 1

Step 1: Since 830 > 235, we apply the division lemma to 830 and 235, to get

830 = 235 x 3 + 125

Step 2: Since the reminder 235 ≠ 0, we apply division lemma to 125 and 235, to get

235 = 125 x 1 + 110

Step 3: We consider the new divisor 125 and the new remainder 110, and apply the division lemma to get

125 = 110 x 1 + 15

We consider the new divisor 110 and the new remainder 15,and apply the division lemma to get

110 = 15 x 7 + 5

We consider the new divisor 15 and the new remainder 5,and apply the division lemma to get

15 = 5 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 830 and 235 is 5

Notice that 5 = HCF(15,5) = HCF(110,15) = HCF(125,110) = HCF(235,125) = HCF(830,235) .

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

Step 1: Since 74 > 5, we apply the division lemma to 74 and 5, to get

74 = 5 x 14 + 4

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 4 and 5, to get

5 = 4 x 1 + 1

Step 3: We consider the new divisor 4 and the new remainder 1, and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5 and 74 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(74,5) .

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

Step 1: Since 132 > 1, we apply the division lemma to 132 and 1, to get

132 = 1 x 132 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 132 is 1

Notice that 1 = HCF(132,1) .

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Frequently Asked Questions on HCF of 830, 235, 74, 132 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 830, 235, 74, 132?

Answer: HCF of 830, 235, 74, 132 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 830, 235, 74, 132 using Euclid's Algorithm?

Answer: For arbitrary numbers 830, 235, 74, 132 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.