Highest Common Factor of 520, 832, 722 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 520, 832, 722 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 520, 832, 722 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 520, 832, 722 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 520, 832, 722 is 2.

HCF(520, 832, 722) = 2

HCF of 520, 832, 722 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 520, 832, 722 is 2.

Highest Common Factor of 520,832,722 using Euclid's algorithm

Highest Common Factor of 520,832,722 is 2

Step 1: Since 832 > 520, we apply the division lemma to 832 and 520, to get

832 = 520 x 1 + 312

Step 2: Since the reminder 520 ≠ 0, we apply division lemma to 312 and 520, to get

520 = 312 x 1 + 208

Step 3: We consider the new divisor 312 and the new remainder 208, and apply the division lemma to get

312 = 208 x 1 + 104

We consider the new divisor 208 and the new remainder 104, and apply the division lemma to get

208 = 104 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 104, the HCF of 520 and 832 is 104

Notice that 104 = HCF(208,104) = HCF(312,208) = HCF(520,312) = HCF(832,520) .

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

Step 1: Since 722 > 104, we apply the division lemma to 722 and 104, to get

722 = 104 x 6 + 98

Step 2: Since the reminder 104 ≠ 0, we apply division lemma to 98 and 104, to get

104 = 98 x 1 + 6

Step 3: We consider the new divisor 98 and the new remainder 6, and apply the division lemma to get

98 = 6 x 16 + 2

We consider the new divisor 6 and the new remainder 2, and apply the division lemma to get

6 = 2 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 104 and 722 is 2

Notice that 2 = HCF(6,2) = HCF(98,6) = HCF(104,98) = HCF(722,104) .

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Frequently Asked Questions on HCF of 520, 832, 722 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 520, 832, 722?

Answer: HCF of 520, 832, 722 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 520, 832, 722 using Euclid's Algorithm?

Answer: For arbitrary numbers 520, 832, 722 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.