Highest Common Factor of 877, 692, 498 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 877, 692, 498 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 877, 692, 498 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 877, 692, 498 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 877, 692, 498 is 1.

HCF(877, 692, 498) = 1

HCF of 877, 692, 498 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 877, 692, 498 is 1.

Highest Common Factor of 877,692,498 using Euclid's algorithm

Highest Common Factor of 877,692,498 is 1

Step 1: Since 877 > 692, we apply the division lemma to 877 and 692, to get

877 = 692 x 1 + 185

Step 2: Since the reminder 692 ≠ 0, we apply division lemma to 185 and 692, to get

692 = 185 x 3 + 137

Step 3: We consider the new divisor 185 and the new remainder 137, and apply the division lemma to get

185 = 137 x 1 + 48

We consider the new divisor 137 and the new remainder 48,and apply the division lemma to get

137 = 48 x 2 + 41

We consider the new divisor 48 and the new remainder 41,and apply the division lemma to get

48 = 41 x 1 + 7

We consider the new divisor 41 and the new remainder 7,and apply the division lemma to get

41 = 7 x 5 + 6

We consider the new divisor 7 and the new remainder 6,and apply the division lemma to get

7 = 6 x 1 + 1

We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get

6 = 1 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 877 and 692 is 1

Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(41,7) = HCF(48,41) = HCF(137,48) = HCF(185,137) = HCF(692,185) = HCF(877,692) .

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

Step 1: Since 498 > 1, we apply the division lemma to 498 and 1, to get

498 = 1 x 498 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 498 is 1

Notice that 1 = HCF(498,1) .

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Frequently Asked Questions on HCF of 877, 692, 498 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 877, 692, 498?

Answer: HCF of 877, 692, 498 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 877, 692, 498 using Euclid's Algorithm?

Answer: For arbitrary numbers 877, 692, 498 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.