Highest Common Factor of 900, 548, 707 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 900, 548, 707 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 900, 548, 707 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 900, 548, 707 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 900, 548, 707 is 1.

HCF(900, 548, 707) = 1

HCF of 900, 548, 707 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 900, 548, 707 is 1.

Highest Common Factor of 900,548,707 using Euclid's algorithm

Highest Common Factor of 900,548,707 is 1

Step 1: Since 900 > 548, we apply the division lemma to 900 and 548, to get

900 = 548 x 1 + 352

Step 2: Since the reminder 548 ≠ 0, we apply division lemma to 352 and 548, to get

548 = 352 x 1 + 196

Step 3: We consider the new divisor 352 and the new remainder 196, and apply the division lemma to get

352 = 196 x 1 + 156

We consider the new divisor 196 and the new remainder 156,and apply the division lemma to get

196 = 156 x 1 + 40

We consider the new divisor 156 and the new remainder 40,and apply the division lemma to get

156 = 40 x 3 + 36

We consider the new divisor 40 and the new remainder 36,and apply the division lemma to get

40 = 36 x 1 + 4

We consider the new divisor 36 and the new remainder 4,and apply the division lemma to get

36 = 4 x 9 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 900 and 548 is 4

Notice that 4 = HCF(36,4) = HCF(40,36) = HCF(156,40) = HCF(196,156) = HCF(352,196) = HCF(548,352) = HCF(900,548) .

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

Step 1: Since 707 > 4, we apply the division lemma to 707 and 4, to get

707 = 4 x 176 + 3

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 3 and 4, to get

4 = 3 x 1 + 1

Step 3: 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 4 and 707 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(707,4) .

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Frequently Asked Questions on HCF of 900, 548, 707 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 900, 548, 707?

Answer: HCF of 900, 548, 707 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 900, 548, 707 using Euclid's Algorithm?

Answer: For arbitrary numbers 900, 548, 707 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.