Highest Common Factor of 169, 1120, 1324 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 169, 1120, 1324 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 169, 1120, 1324 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 169, 1120, 1324 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 169, 1120, 1324 is 1.

HCF(169, 1120, 1324) = 1

HCF of 169, 1120, 1324 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 169, 1120, 1324 is 1.

Highest Common Factor of 169,1120,1324 using Euclid's algorithm

Highest Common Factor of 169,1120,1324 is 1

Step 1: Since 1120 > 169, we apply the division lemma to 1120 and 169, to get

1120 = 169 x 6 + 106

Step 2: Since the reminder 169 ≠ 0, we apply division lemma to 106 and 169, to get

169 = 106 x 1 + 63

Step 3: We consider the new divisor 106 and the new remainder 63, and apply the division lemma to get

106 = 63 x 1 + 43

We consider the new divisor 63 and the new remainder 43,and apply the division lemma to get

63 = 43 x 1 + 20

We consider the new divisor 43 and the new remainder 20,and apply the division lemma to get

43 = 20 x 2 + 3

We consider the new divisor 20 and the new remainder 3,and apply the division lemma to get

20 = 3 x 6 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 169 and 1120 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(20,3) = HCF(43,20) = HCF(63,43) = HCF(106,63) = HCF(169,106) = HCF(1120,169) .

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

Step 1: Since 1324 > 1, we apply the division lemma to 1324 and 1, to get

1324 = 1 x 1324 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 1324 is 1

Notice that 1 = HCF(1324,1) .

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Frequently Asked Questions on HCF of 169, 1120, 1324 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 169, 1120, 1324?

Answer: HCF of 169, 1120, 1324 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 169, 1120, 1324 using Euclid's Algorithm?

Answer: For arbitrary numbers 169, 1120, 1324 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.