Highest Common Factor of 985, 374, 40 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 985, 374, 40 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 985, 374, 40 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 985, 374, 40 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 985, 374, 40 is 1.

HCF(985, 374, 40) = 1

HCF of 985, 374, 40 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 985, 374, 40 is 1.

Highest Common Factor of 985,374,40 using Euclid's algorithm

Highest Common Factor of 985,374,40 is 1

Step 1: Since 985 > 374, we apply the division lemma to 985 and 374, to get

985 = 374 x 2 + 237

Step 2: Since the reminder 374 ≠ 0, we apply division lemma to 237 and 374, to get

374 = 237 x 1 + 137

Step 3: We consider the new divisor 237 and the new remainder 137, and apply the division lemma to get

237 = 137 x 1 + 100

We consider the new divisor 137 and the new remainder 100,and apply the division lemma to get

137 = 100 x 1 + 37

We consider the new divisor 100 and the new remainder 37,and apply the division lemma to get

100 = 37 x 2 + 26

We consider the new divisor 37 and the new remainder 26,and apply the division lemma to get

37 = 26 x 1 + 11

We consider the new divisor 26 and the new remainder 11,and apply the division lemma to get

26 = 11 x 2 + 4

We consider the new divisor 11 and the new remainder 4,and apply the division lemma to get

11 = 4 x 2 + 3

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

4 = 3 x 1 + 1

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

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 985 and 374 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(11,4) = HCF(26,11) = HCF(37,26) = HCF(100,37) = HCF(137,100) = HCF(237,137) = HCF(374,237) = HCF(985,374) .

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

Step 1: Since 40 > 1, we apply the division lemma to 40 and 1, to get

40 = 1 x 40 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 40 is 1

Notice that 1 = HCF(40,1) .

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Frequently Asked Questions on HCF of 985, 374, 40 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 985, 374, 40?

Answer: HCF of 985, 374, 40 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 985, 374, 40 using Euclid's Algorithm?

Answer: For arbitrary numbers 985, 374, 40 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.