Highest Common Factor of 970, 596, 145 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 970, 596, 145 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 970, 596, 145 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 970, 596, 145 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 970, 596, 145 is 1.

HCF(970, 596, 145) = 1

HCF of 970, 596, 145 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 970, 596, 145 is 1.

Highest Common Factor of 970,596,145 using Euclid's algorithm

Highest Common Factor of 970,596,145 is 1

Step 1: Since 970 > 596, we apply the division lemma to 970 and 596, to get

970 = 596 x 1 + 374

Step 2: Since the reminder 596 ≠ 0, we apply division lemma to 374 and 596, to get

596 = 374 x 1 + 222

Step 3: We consider the new divisor 374 and the new remainder 222, and apply the division lemma to get

374 = 222 x 1 + 152

We consider the new divisor 222 and the new remainder 152,and apply the division lemma to get

222 = 152 x 1 + 70

We consider the new divisor 152 and the new remainder 70,and apply the division lemma to get

152 = 70 x 2 + 12

We consider the new divisor 70 and the new remainder 12,and apply the division lemma to get

70 = 12 x 5 + 10

We consider the new divisor 12 and the new remainder 10,and apply the division lemma to get

12 = 10 x 1 + 2

We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get

10 = 2 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 970 and 596 is 2

Notice that 2 = HCF(10,2) = HCF(12,10) = HCF(70,12) = HCF(152,70) = HCF(222,152) = HCF(374,222) = HCF(596,374) = HCF(970,596) .

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

Step 1: Since 145 > 2, we apply the division lemma to 145 and 2, to get

145 = 2 x 72 + 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 145 is 1

Notice that 1 = HCF(2,1) = HCF(145,2) .

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Frequently Asked Questions on HCF of 970, 596, 145 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 970, 596, 145?

Answer: HCF of 970, 596, 145 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 970, 596, 145 using Euclid's Algorithm?

Answer: For arbitrary numbers 970, 596, 145 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.