Highest Common Factor of 375, 512, 700 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 375, 512, 700 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 375, 512, 700 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 375, 512, 700 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 375, 512, 700 is 1.

HCF(375, 512, 700) = 1

HCF of 375, 512, 700 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 375, 512, 700 is 1.

Highest Common Factor of 375,512,700 using Euclid's algorithm

Highest Common Factor of 375,512,700 is 1

Step 1: Since 512 > 375, we apply the division lemma to 512 and 375, to get

512 = 375 x 1 + 137

Step 2: Since the reminder 375 ≠ 0, we apply division lemma to 137 and 375, to get

375 = 137 x 2 + 101

Step 3: We consider the new divisor 137 and the new remainder 101, and apply the division lemma to get

137 = 101 x 1 + 36

We consider the new divisor 101 and the new remainder 36,and apply the division lemma to get

101 = 36 x 2 + 29

We consider the new divisor 36 and the new remainder 29,and apply the division lemma to get

36 = 29 x 1 + 7

We consider the new divisor 29 and the new remainder 7,and apply the division lemma to get

29 = 7 x 4 + 1

We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get

7 = 1 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 375 and 512 is 1

Notice that 1 = HCF(7,1) = HCF(29,7) = HCF(36,29) = HCF(101,36) = HCF(137,101) = HCF(375,137) = HCF(512,375) .

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

Step 1: Since 700 > 1, we apply the division lemma to 700 and 1, to get

700 = 1 x 700 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 700 is 1

Notice that 1 = HCF(700,1) .

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Frequently Asked Questions on HCF of 375, 512, 700 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 375, 512, 700?

Answer: HCF of 375, 512, 700 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 375, 512, 700 using Euclid's Algorithm?

Answer: For arbitrary numbers 375, 512, 700 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.