Highest Common Factor of 300, 460, 210 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 300, 460, 210 i.e. 10 the largest integer that leaves a remainder zero for all numbers.
HCF of 300, 460, 210 is 10 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 300, 460, 210 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 300, 460, 210 is 10.
HCF(300, 460, 210) = 10
HCF of 300, 460, 210 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 300, 460, 210 is 10.
Highest Common Factor of 300,460,210 is 10
Step 1: Since 460 > 300, we apply the division lemma to 460 and 300, to get
460 = 300 x 1 + 160
Step 2: Since the reminder 300 ≠ 0, we apply division lemma to 160 and 300, to get
300 = 160 x 1 + 140
Step 3: We consider the new divisor 160 and the new remainder 140, and apply the division lemma to get
160 = 140 x 1 + 20
We consider the new divisor 140 and the new remainder 20, and apply the division lemma to get
140 = 20 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 20, the HCF of 300 and 460 is 20
Notice that 20 = HCF(140,20) = HCF(160,140) = HCF(300,160) = HCF(460,300) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 210 > 20, we apply the division lemma to 210 and 20, to get
210 = 20 x 10 + 10
Step 2: Since the reminder 20 ≠ 0, we apply division lemma to 10 and 20, to get
20 = 10 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 20 and 210 is 10
Notice that 10 = HCF(20,10) = HCF(210,20) .
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Frequently Asked Questions on HCF of 300, 460, 210 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 300, 460, 210?
Answer: HCF of 300, 460, 210 is 10 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 300, 460, 210 using Euclid's Algorithm?
Answer: For arbitrary numbers 300, 460, 210 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.