Highest Common Factor of 990, 717, 240 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 990, 717, 240 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 990, 717, 240 is 3 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 990, 717, 240 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 990, 717, 240 is 3.
HCF(990, 717, 240) = 3
HCF of 990, 717, 240 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 990, 717, 240 is 3.
Highest Common Factor of 990,717,240 is 3
Step 1: Since 990 > 717, we apply the division lemma to 990 and 717, to get
990 = 717 x 1 + 273
Step 2: Since the reminder 717 ≠ 0, we apply division lemma to 273 and 717, to get
717 = 273 x 2 + 171
Step 3: We consider the new divisor 273 and the new remainder 171, and apply the division lemma to get
273 = 171 x 1 + 102
We consider the new divisor 171 and the new remainder 102,and apply the division lemma to get
171 = 102 x 1 + 69
We consider the new divisor 102 and the new remainder 69,and apply the division lemma to get
102 = 69 x 1 + 33
We consider the new divisor 69 and the new remainder 33,and apply the division lemma to get
69 = 33 x 2 + 3
We consider the new divisor 33 and the new remainder 3,and apply the division lemma to get
33 = 3 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 990 and 717 is 3
Notice that 3 = HCF(33,3) = HCF(69,33) = HCF(102,69) = HCF(171,102) = HCF(273,171) = HCF(717,273) = HCF(990,717) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 240 > 3, we apply the division lemma to 240 and 3, to get
240 = 3 x 80 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 240 is 3
Notice that 3 = HCF(240,3) .
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Frequently Asked Questions on HCF of 990, 717, 240 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 990, 717, 240?
Answer: HCF of 990, 717, 240 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 990, 717, 240 using Euclid's Algorithm?
Answer: For arbitrary numbers 990, 717, 240 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
