Highest Common Factor of 856, 525, 400 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 856, 525, 400 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 856, 525, 400 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 856, 525, 400 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 856, 525, 400 is 1.

HCF(856, 525, 400) = 1

HCF of 856, 525, 400 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 856, 525, 400 is 1.

Highest Common Factor of 856,525,400 using Euclid's algorithm

Highest Common Factor of 856,525,400 is 1

Step 1: Since 856 > 525, we apply the division lemma to 856 and 525, to get

856 = 525 x 1 + 331

Step 2: Since the reminder 525 ≠ 0, we apply division lemma to 331 and 525, to get

525 = 331 x 1 + 194

Step 3: We consider the new divisor 331 and the new remainder 194, and apply the division lemma to get

331 = 194 x 1 + 137

We consider the new divisor 194 and the new remainder 137,and apply the division lemma to get

194 = 137 x 1 + 57

We consider the new divisor 137 and the new remainder 57,and apply the division lemma to get

137 = 57 x 2 + 23

We consider the new divisor 57 and the new remainder 23,and apply the division lemma to get

57 = 23 x 2 + 11

We consider the new divisor 23 and the new remainder 11,and apply the division lemma to get

23 = 11 x 2 + 1

We consider the new divisor 11 and the new remainder 1,and apply the division lemma to get

11 = 1 x 11 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 856 and 525 is 1

Notice that 1 = HCF(11,1) = HCF(23,11) = HCF(57,23) = HCF(137,57) = HCF(194,137) = HCF(331,194) = HCF(525,331) = HCF(856,525) .

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

Step 1: Since 400 > 1, we apply the division lemma to 400 and 1, to get

400 = 1 x 400 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 400 is 1

Notice that 1 = HCF(400,1) .

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Frequently Asked Questions on HCF of 856, 525, 400 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 856, 525, 400?

Answer: HCF of 856, 525, 400 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 856, 525, 400 using Euclid's Algorithm?

Answer: For arbitrary numbers 856, 525, 400 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.