Highest Common Factor of 964, 612, 907 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 964, 612, 907 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 964, 612, 907 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 964, 612, 907 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 964, 612, 907 is 1.

HCF(964, 612, 907) = 1

HCF of 964, 612, 907 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 964, 612, 907 is 1.

Highest Common Factor of 964,612,907 using Euclid's algorithm

Highest Common Factor of 964,612,907 is 1

Step 1: Since 964 > 612, we apply the division lemma to 964 and 612, to get

964 = 612 x 1 + 352

Step 2: Since the reminder 612 ≠ 0, we apply division lemma to 352 and 612, to get

612 = 352 x 1 + 260

Step 3: We consider the new divisor 352 and the new remainder 260, and apply the division lemma to get

352 = 260 x 1 + 92

We consider the new divisor 260 and the new remainder 92,and apply the division lemma to get

260 = 92 x 2 + 76

We consider the new divisor 92 and the new remainder 76,and apply the division lemma to get

92 = 76 x 1 + 16

We consider the new divisor 76 and the new remainder 16,and apply the division lemma to get

76 = 16 x 4 + 12

We consider the new divisor 16 and the new remainder 12,and apply the division lemma to get

16 = 12 x 1 + 4

We consider the new divisor 12 and the new remainder 4,and apply the division lemma to get

12 = 4 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 964 and 612 is 4

Notice that 4 = HCF(12,4) = HCF(16,12) = HCF(76,16) = HCF(92,76) = HCF(260,92) = HCF(352,260) = HCF(612,352) = HCF(964,612) .

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

Step 1: Since 907 > 4, we apply the division lemma to 907 and 4, to get

907 = 4 x 226 + 3

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 3 and 4, to get

4 = 3 x 1 + 1

Step 3: 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 4 and 907 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(907,4) .

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Frequently Asked Questions on HCF of 964, 612, 907 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 964, 612, 907?

Answer: HCF of 964, 612, 907 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 964, 612, 907 using Euclid's Algorithm?

Answer: For arbitrary numbers 964, 612, 907 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.