Highest Common Factor of 990, 275, 234 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, 275, 234 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 990, 275, 234 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 990, 275, 234 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, 275, 234 is 1.
HCF(990, 275, 234) = 1
HCF of 990, 275, 234 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, 275, 234 is 1.
Highest Common Factor of 990,275,234 is 1
Step 1: Since 990 > 275, we apply the division lemma to 990 and 275, to get
990 = 275 x 3 + 165
Step 2: Since the reminder 275 ≠ 0, we apply division lemma to 165 and 275, to get
275 = 165 x 1 + 110
Step 3: We consider the new divisor 165 and the new remainder 110, and apply the division lemma to get
165 = 110 x 1 + 55
We consider the new divisor 110 and the new remainder 55, and apply the division lemma to get
110 = 55 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 55, the HCF of 990 and 275 is 55
Notice that 55 = HCF(110,55) = HCF(165,110) = HCF(275,165) = HCF(990,275) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 234 > 55, we apply the division lemma to 234 and 55, to get
234 = 55 x 4 + 14
Step 2: Since the reminder 55 ≠ 0, we apply division lemma to 14 and 55, to get
55 = 14 x 3 + 13
Step 3: We consider the new divisor 14 and the new remainder 13, and apply the division lemma to get
14 = 13 x 1 + 1
We consider the new divisor 13 and the new remainder 1, and apply the division lemma to get
13 = 1 x 13 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 55 and 234 is 1
Notice that 1 = HCF(13,1) = HCF(14,13) = HCF(55,14) = HCF(234,55) .
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Frequently Asked Questions on HCF of 990, 275, 234 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, 275, 234?
Answer: HCF of 990, 275, 234 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 990, 275, 234 using Euclid's Algorithm?
Answer: For arbitrary numbers 990, 275, 234 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
