Highest Common Factor of 953, 698 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 953, 698 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 953, 698 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 953, 698 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 953, 698 is 1.

HCF(953, 698) = 1

HCF of 953, 698 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 953, 698 is 1.

Highest Common Factor of 953,698 using Euclid's algorithm

Highest Common Factor of 953,698 is 1

Step 1: Since 953 > 698, we apply the division lemma to 953 and 698, to get

953 = 698 x 1 + 255

Step 2: Since the reminder 698 ≠ 0, we apply division lemma to 255 and 698, to get

698 = 255 x 2 + 188

Step 3: We consider the new divisor 255 and the new remainder 188, and apply the division lemma to get

255 = 188 x 1 + 67

We consider the new divisor 188 and the new remainder 67,and apply the division lemma to get

188 = 67 x 2 + 54

We consider the new divisor 67 and the new remainder 54,and apply the division lemma to get

67 = 54 x 1 + 13

We consider the new divisor 54 and the new remainder 13,and apply the division lemma to get

54 = 13 x 4 + 2

We consider the new divisor 13 and the new remainder 2,and apply the division lemma to get

13 = 2 x 6 + 1

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 953 and 698 is 1

Notice that 1 = HCF(2,1) = HCF(13,2) = HCF(54,13) = HCF(67,54) = HCF(188,67) = HCF(255,188) = HCF(698,255) = HCF(953,698) .

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Frequently Asked Questions on HCF of 953, 698 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 953, 698?

Answer: HCF of 953, 698 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 953, 698 using Euclid's Algorithm?

Answer: For arbitrary numbers 953, 698 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.