Highest Common Factor of 414, 975, 310 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 414, 975, 310 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 414, 975, 310 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 414, 975, 310 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 414, 975, 310 is 1.

HCF(414, 975, 310) = 1

HCF of 414, 975, 310 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 414, 975, 310 is 1.

Highest Common Factor of 414,975,310 using Euclid's algorithm

Highest Common Factor of 414,975,310 is 1

Step 1: Since 975 > 414, we apply the division lemma to 975 and 414, to get

975 = 414 x 2 + 147

Step 2: Since the reminder 414 ≠ 0, we apply division lemma to 147 and 414, to get

414 = 147 x 2 + 120

Step 3: We consider the new divisor 147 and the new remainder 120, and apply the division lemma to get

147 = 120 x 1 + 27

We consider the new divisor 120 and the new remainder 27,and apply the division lemma to get

120 = 27 x 4 + 12

We consider the new divisor 27 and the new remainder 12,and apply the division lemma to get

27 = 12 x 2 + 3

We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get

12 = 3 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 414 and 975 is 3

Notice that 3 = HCF(12,3) = HCF(27,12) = HCF(120,27) = HCF(147,120) = HCF(414,147) = HCF(975,414) .

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

Step 1: Since 310 > 3, we apply the division lemma to 310 and 3, to get

310 = 3 x 103 + 1

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, 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 3 and 310 is 1

Notice that 1 = HCF(3,1) = HCF(310,3) .

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Frequently Asked Questions on HCF of 414, 975, 310 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 414, 975, 310?

Answer: HCF of 414, 975, 310 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 414, 975, 310 using Euclid's Algorithm?

Answer: For arbitrary numbers 414, 975, 310 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.