Highest Common Factor of 658, 436, 749 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 658, 436, 749 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 658, 436, 749 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 658, 436, 749 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 658, 436, 749 is 1.

HCF(658, 436, 749) = 1

HCF of 658, 436, 749 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 658, 436, 749 is 1.

Highest Common Factor of 658,436,749 using Euclid's algorithm

Highest Common Factor of 658,436,749 is 1

Step 1: Since 658 > 436, we apply the division lemma to 658 and 436, to get

658 = 436 x 1 + 222

Step 2: Since the reminder 436 ≠ 0, we apply division lemma to 222 and 436, to get

436 = 222 x 1 + 214

Step 3: We consider the new divisor 222 and the new remainder 214, and apply the division lemma to get

222 = 214 x 1 + 8

We consider the new divisor 214 and the new remainder 8,and apply the division lemma to get

214 = 8 x 26 + 6

We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get

8 = 6 x 1 + 2

We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get

6 = 2 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 658 and 436 is 2

Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(214,8) = HCF(222,214) = HCF(436,222) = HCF(658,436) .

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

Step 1: Since 749 > 2, we apply the division lemma to 749 and 2, to get

749 = 2 x 374 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 749 is 1

Notice that 1 = HCF(2,1) = HCF(749,2) .

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Frequently Asked Questions on HCF of 658, 436, 749 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 658, 436, 749?

Answer: HCF of 658, 436, 749 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 658, 436, 749 using Euclid's Algorithm?

Answer: For arbitrary numbers 658, 436, 749 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.