Highest Common Factor of 670, 856, 33 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 670, 856, 33 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 670, 856, 33 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 670, 856, 33 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 670, 856, 33 is 1.

HCF(670, 856, 33) = 1

HCF of 670, 856, 33 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 670, 856, 33 is 1.

Highest Common Factor of 670,856,33 using Euclid's algorithm

Highest Common Factor of 670,856,33 is 1

Step 1: Since 856 > 670, we apply the division lemma to 856 and 670, to get

856 = 670 x 1 + 186

Step 2: Since the reminder 670 ≠ 0, we apply division lemma to 186 and 670, to get

670 = 186 x 3 + 112

Step 3: We consider the new divisor 186 and the new remainder 112, and apply the division lemma to get

186 = 112 x 1 + 74

We consider the new divisor 112 and the new remainder 74,and apply the division lemma to get

112 = 74 x 1 + 38

We consider the new divisor 74 and the new remainder 38,and apply the division lemma to get

74 = 38 x 1 + 36

We consider the new divisor 38 and the new remainder 36,and apply the division lemma to get

38 = 36 x 1 + 2

We consider the new divisor 36 and the new remainder 2,and apply the division lemma to get

36 = 2 x 18 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 670 and 856 is 2

Notice that 2 = HCF(36,2) = HCF(38,36) = HCF(74,38) = HCF(112,74) = HCF(186,112) = HCF(670,186) = HCF(856,670) .

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

Step 1: Since 33 > 2, we apply the division lemma to 33 and 2, to get

33 = 2 x 16 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 33 is 1

Notice that 1 = HCF(2,1) = HCF(33,2) .

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Frequently Asked Questions on HCF of 670, 856, 33 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 670, 856, 33?

Answer: HCF of 670, 856, 33 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 670, 856, 33 using Euclid's Algorithm?

Answer: For arbitrary numbers 670, 856, 33 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.