Highest Common Factor of 209, 962, 748 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 209, 962, 748 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 209, 962, 748 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 209, 962, 748 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 209, 962, 748 is 1.

HCF(209, 962, 748) = 1

HCF of 209, 962, 748 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 209, 962, 748 is 1.

Highest Common Factor of 209,962,748 using Euclid's algorithm

Highest Common Factor of 209,962,748 is 1

Step 1: Since 962 > 209, we apply the division lemma to 962 and 209, to get

962 = 209 x 4 + 126

Step 2: Since the reminder 209 ≠ 0, we apply division lemma to 126 and 209, to get

209 = 126 x 1 + 83

Step 3: We consider the new divisor 126 and the new remainder 83, and apply the division lemma to get

126 = 83 x 1 + 43

We consider the new divisor 83 and the new remainder 43,and apply the division lemma to get

83 = 43 x 1 + 40

We consider the new divisor 43 and the new remainder 40,and apply the division lemma to get

43 = 40 x 1 + 3

We consider the new divisor 40 and the new remainder 3,and apply the division lemma to get

40 = 3 x 13 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma 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 209 and 962 is 1

Notice that 1 = HCF(3,1) = HCF(40,3) = HCF(43,40) = HCF(83,43) = HCF(126,83) = HCF(209,126) = HCF(962,209) .

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

Step 1: Since 748 > 1, we apply the division lemma to 748 and 1, to get

748 = 1 x 748 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 748 is 1

Notice that 1 = HCF(748,1) .

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Frequently Asked Questions on HCF of 209, 962, 748 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 209, 962, 748?

Answer: HCF of 209, 962, 748 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 209, 962, 748 using Euclid's Algorithm?

Answer: For arbitrary numbers 209, 962, 748 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.