Highest Common Factor of 210, 990, 435 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 210, 990, 435 i.e. 15 the largest integer that leaves a remainder zero for all numbers.
HCF of 210, 990, 435 is 15 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 210, 990, 435 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 210, 990, 435 is 15.
HCF(210, 990, 435) = 15
HCF of 210, 990, 435 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 210, 990, 435 is 15.
Highest Common Factor of 210,990,435 is 15
Step 1: Since 990 > 210, we apply the division lemma to 990 and 210, to get
990 = 210 x 4 + 150
Step 2: Since the reminder 210 ≠ 0, we apply division lemma to 150 and 210, to get
210 = 150 x 1 + 60
Step 3: We consider the new divisor 150 and the new remainder 60, and apply the division lemma to get
150 = 60 x 2 + 30
We consider the new divisor 60 and the new remainder 30, and apply the division lemma to get
60 = 30 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 30, the HCF of 210 and 990 is 30
Notice that 30 = HCF(60,30) = HCF(150,60) = HCF(210,150) = HCF(990,210) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 435 > 30, we apply the division lemma to 435 and 30, to get
435 = 30 x 14 + 15
Step 2: Since the reminder 30 ≠ 0, we apply division lemma to 15 and 30, to get
30 = 15 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 30 and 435 is 15
Notice that 15 = HCF(30,15) = HCF(435,30) .
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Frequently Asked Questions on HCF of 210, 990, 435 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 210, 990, 435?
Answer: HCF of 210, 990, 435 is 15 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 210, 990, 435 using Euclid's Algorithm?
Answer: For arbitrary numbers 210, 990, 435 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.