Highest Common Factor of 991, 717, 207, 364 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

Highest common factor (HCF) of 991, 717, 207, 364 is 1.

Step 1: Since 991 > 717, we apply the division lemma to 991 and 717, to get

991 = 717 x 1 + 274

Step 2: Since the reminder 717 ≠ 0, we apply division lemma to 274 and 717, to get

717 = 274 x 2 + 169

Step 3: We consider the new divisor 274 and the new remainder 169, and apply the division lemma to get

274 = 169 x 1 + 105

We consider the new divisor 169 and the new remainder 105,and apply the division lemma to get

169 = 105 x 1 + 64

We consider the new divisor 105 and the new remainder 64,and apply the division lemma to get

105 = 64 x 1 + 41

We consider the new divisor 64 and the new remainder 41,and apply the division lemma to get

64 = 41 x 1 + 23

We consider the new divisor 41 and the new remainder 23,and apply the division lemma to get

41 = 23 x 1 + 18

We consider the new divisor 23 and the new remainder 18,and apply the division lemma to get

23 = 18 x 1 + 5

We consider the new divisor 18 and the new remainder 5,and apply the division lemma to get

18 = 5 x 3 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 991 and 717 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(18,5) = HCF(23,18) = HCF(41,23) = HCF(64,41) = HCF(105,64) = HCF(169,105) = HCF(274,169) = HCF(717,274) = HCF(991,717) .

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

Step 1: Since 207 > 1, we apply the division lemma to 207 and 1, to get

207 = 1 x 207 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 207 is 1

Notice that 1 = HCF(207,1) .

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

Step 1: Since 364 > 1, we apply the division lemma to 364 and 1, to get

364 = 1 x 364 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 364 is 1

Notice that 1 = HCF(364,1) .

Here are some samples of HCF using Euclid's Algorithm calculations.

• HCF of 367, 671, 866, 196
• HCF of 482, 986, 355, 153
• HCF of 545, 861, 759, 419
• HCF of 882, 538, 235, 566
• HCF of 472, 577, 897, 898

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 991, 717, 207, 364?

Answer: HCF of 991, 717, 207, 364 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 991, 717, 207, 364 using Euclid's Algorithm?

Answer: For arbitrary numbers 991, 717, 207, 364 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.