Highest Common Factor of 310, 757, 98 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 310, 757, 98 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 310, 757, 98 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 310, 757, 98 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 310, 757, 98 is 1.

HCF(310, 757, 98) = 1

HCF of 310, 757, 98 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 310, 757, 98 is 1.

Highest Common Factor of 310,757,98 using Euclid's algorithm

Highest Common Factor of 310,757,98 is 1

Step 1: Since 757 > 310, we apply the division lemma to 757 and 310, to get

757 = 310 x 2 + 137

Step 2: Since the reminder 310 ≠ 0, we apply division lemma to 137 and 310, to get

310 = 137 x 2 + 36

Step 3: We consider the new divisor 137 and the new remainder 36, and apply the division lemma to get

137 = 36 x 3 + 29

We consider the new divisor 36 and the new remainder 29,and apply the division lemma to get

36 = 29 x 1 + 7

We consider the new divisor 29 and the new remainder 7,and apply the division lemma to get

29 = 7 x 4 + 1

We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get

7 = 1 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 310 and 757 is 1

Notice that 1 = HCF(7,1) = HCF(29,7) = HCF(36,29) = HCF(137,36) = HCF(310,137) = HCF(757,310) .

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

Step 1: Since 98 > 1, we apply the division lemma to 98 and 1, to get

98 = 1 x 98 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 98 is 1

Notice that 1 = HCF(98,1) .

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Frequently Asked Questions on HCF of 310, 757, 98 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 310, 757, 98?

Answer: HCF of 310, 757, 98 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 310, 757, 98 using Euclid's Algorithm?

Answer: For arbitrary numbers 310, 757, 98 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.