Highest Common Factor of 625, 742, 684 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 625, 742, 684 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 625, 742, 684 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 625, 742, 684 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 625, 742, 684 is 1.

HCF(625, 742, 684) = 1

HCF of 625, 742, 684 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 625, 742, 684 is 1.

Highest Common Factor of 625,742,684 using Euclid's algorithm

Highest Common Factor of 625,742,684 is 1

Step 1: Since 742 > 625, we apply the division lemma to 742 and 625, to get

742 = 625 x 1 + 117

Step 2: Since the reminder 625 ≠ 0, we apply division lemma to 117 and 625, to get

625 = 117 x 5 + 40

Step 3: We consider the new divisor 117 and the new remainder 40, and apply the division lemma to get

117 = 40 x 2 + 37

We consider the new divisor 40 and the new remainder 37,and apply the division lemma to get

40 = 37 x 1 + 3

We consider the new divisor 37 and the new remainder 3,and apply the division lemma to get

37 = 3 x 12 + 1

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 625 and 742 is 1

Notice that 1 = HCF(3,1) = HCF(37,3) = HCF(40,37) = HCF(117,40) = HCF(625,117) = HCF(742,625) .

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

Step 1: Since 684 > 1, we apply the division lemma to 684 and 1, to get

684 = 1 x 684 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 684 is 1

Notice that 1 = HCF(684,1) .

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Frequently Asked Questions on HCF of 625, 742, 684 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 625, 742, 684?

Answer: HCF of 625, 742, 684 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 625, 742, 684 using Euclid's Algorithm?

Answer: For arbitrary numbers 625, 742, 684 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.