Highest Common Factor of 904, 714, 64 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 904, 714, 64 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 904, 714, 64 is 2 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 904, 714, 64 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 904, 714, 64 is 2.

HCF(904, 714, 64) = 2

HCF of 904, 714, 64 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 904, 714, 64 is 2.

Highest Common Factor of 904,714,64 using Euclid's algorithm

Highest Common Factor of 904,714,64 is 2

Step 1: Since 904 > 714, we apply the division lemma to 904 and 714, to get

904 = 714 x 1 + 190

Step 2: Since the reminder 714 ≠ 0, we apply division lemma to 190 and 714, to get

714 = 190 x 3 + 144

Step 3: We consider the new divisor 190 and the new remainder 144, and apply the division lemma to get

190 = 144 x 1 + 46

We consider the new divisor 144 and the new remainder 46,and apply the division lemma to get

144 = 46 x 3 + 6

We consider the new divisor 46 and the new remainder 6,and apply the division lemma to get

46 = 6 x 7 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 904 and 714 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(46,6) = HCF(144,46) = HCF(190,144) = HCF(714,190) = HCF(904,714) .

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

Step 1: Since 64 > 2, we apply the division lemma to 64 and 2, to get

64 = 2 x 32 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 64 is 2

Notice that 2 = HCF(64,2) .

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Frequently Asked Questions on HCF of 904, 714, 64 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 904, 714, 64?

Answer: HCF of 904, 714, 64 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 904, 714, 64 using Euclid's Algorithm?

Answer: For arbitrary numbers 904, 714, 64 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.