Highest Common Factor of 840, 985, 352 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 840, 985, 352 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 840, 985, 352 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 840, 985, 352 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 840, 985, 352 is 1.

HCF(840, 985, 352) = 1

HCF of 840, 985, 352 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 840, 985, 352 is 1.

Highest Common Factor of 840,985,352 using Euclid's algorithm

Highest Common Factor of 840,985,352 is 1

Step 1: Since 985 > 840, we apply the division lemma to 985 and 840, to get

985 = 840 x 1 + 145

Step 2: Since the reminder 840 ≠ 0, we apply division lemma to 145 and 840, to get

840 = 145 x 5 + 115

Step 3: We consider the new divisor 145 and the new remainder 115, and apply the division lemma to get

145 = 115 x 1 + 30

We consider the new divisor 115 and the new remainder 30,and apply the division lemma to get

115 = 30 x 3 + 25

We consider the new divisor 30 and the new remainder 25,and apply the division lemma to get

30 = 25 x 1 + 5

We consider the new divisor 25 and the new remainder 5,and apply the division lemma to get

25 = 5 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 840 and 985 is 5

Notice that 5 = HCF(25,5) = HCF(30,25) = HCF(115,30) = HCF(145,115) = HCF(840,145) = HCF(985,840) .

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

Step 1: Since 352 > 5, we apply the division lemma to 352 and 5, to get

352 = 5 x 70 + 2

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

5 = 2 x 2 + 1

Step 3: 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 5 and 352 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(352,5) .

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Frequently Asked Questions on HCF of 840, 985, 352 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 840, 985, 352?

Answer: HCF of 840, 985, 352 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 840, 985, 352 using Euclid's Algorithm?

Answer: For arbitrary numbers 840, 985, 352 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.