Highest Common Factor of 990, 705, 888 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, 705, 888 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 990, 705, 888 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, 705, 888 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, 705, 888 is 3.
HCF(990, 705, 888) = 3
HCF of 990, 705, 888 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, 705, 888 is 3.
Highest Common Factor of 990,705,888 is 3
Step 1: Since 990 > 705, we apply the division lemma to 990 and 705, to get
990 = 705 x 1 + 285
Step 2: Since the reminder 705 ≠ 0, we apply division lemma to 285 and 705, to get
705 = 285 x 2 + 135
Step 3: We consider the new divisor 285 and the new remainder 135, and apply the division lemma to get
285 = 135 x 2 + 15
We consider the new divisor 135 and the new remainder 15, and apply the division lemma to get
135 = 15 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 990 and 705 is 15
Notice that 15 = HCF(135,15) = HCF(285,135) = HCF(705,285) = HCF(990,705) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 888 > 15, we apply the division lemma to 888 and 15, to get
888 = 15 x 59 + 3
Step 2: Since the reminder 15 ≠ 0, we apply division lemma to 3 and 15, to get
15 = 3 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 15 and 888 is 3
Notice that 3 = HCF(15,3) = HCF(888,15) .
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Frequently Asked Questions on HCF of 990, 705, 888 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, 705, 888?
Answer: HCF of 990, 705, 888 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 990, 705, 888 using Euclid's Algorithm?
Answer: For arbitrary numbers 990, 705, 888 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.