Highest Common Factor of 225, 807, 340 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 225, 807, 340 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 225, 807, 340 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 225, 807, 340 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 225, 807, 340 is 1.

HCF(225, 807, 340) = 1

HCF of 225, 807, 340 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 225, 807, 340 is 1.

Highest Common Factor of 225,807,340 using Euclid's algorithm

Highest Common Factor of 225,807,340 is 1

Step 1: Since 807 > 225, we apply the division lemma to 807 and 225, to get

807 = 225 x 3 + 132

Step 2: Since the reminder 225 ≠ 0, we apply division lemma to 132 and 225, to get

225 = 132 x 1 + 93

Step 3: We consider the new divisor 132 and the new remainder 93, and apply the division lemma to get

132 = 93 x 1 + 39

We consider the new divisor 93 and the new remainder 39,and apply the division lemma to get

93 = 39 x 2 + 15

We consider the new divisor 39 and the new remainder 15,and apply the division lemma to get

39 = 15 x 2 + 9

We consider the new divisor 15 and the new remainder 9,and apply the division lemma to get

15 = 9 x 1 + 6

We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get

9 = 6 x 1 + 3

We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get

6 = 3 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 225 and 807 is 3

Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(15,9) = HCF(39,15) = HCF(93,39) = HCF(132,93) = HCF(225,132) = HCF(807,225) .

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

Step 1: Since 340 > 3, we apply the division lemma to 340 and 3, to get

340 = 3 x 113 + 1

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, 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 3 and 340 is 1

Notice that 1 = HCF(3,1) = HCF(340,3) .

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Frequently Asked Questions on HCF of 225, 807, 340 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 225, 807, 340?

Answer: HCF of 225, 807, 340 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 225, 807, 340 using Euclid's Algorithm?

Answer: For arbitrary numbers 225, 807, 340 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.