Highest Common Factor of 240, 312, 21, 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 240, 312, 21, 210 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 240, 312, 21, 210 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 240, 312, 21, 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 240, 312, 21, 210 is 3.
HCF(240, 312, 21, 210) = 3
HCF of 240, 312, 21, 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 240, 312, 21, 210 is 3.
Highest Common Factor of 240,312,21,210 is 3
Step 1: Since 312 > 240, we apply the division lemma to 312 and 240, to get
312 = 240 x 1 + 72
Step 2: Since the reminder 240 ≠ 0, we apply division lemma to 72 and 240, to get
240 = 72 x 3 + 24
Step 3: We consider the new divisor 72 and the new remainder 24, and apply the division lemma to get
72 = 24 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 24, the HCF of 240 and 312 is 24
Notice that 24 = HCF(72,24) = HCF(240,72) = HCF(312,240) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 24 > 21, we apply the division lemma to 24 and 21, to get
24 = 21 x 1 + 3
Step 2: Since the reminder 21 ≠ 0, we apply division lemma to 3 and 21, to get
21 = 3 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 24 and 21 is 3
Notice that 3 = HCF(21,3) = HCF(24,21) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 210 > 3, we apply the division lemma to 210 and 3, to get
210 = 3 x 70 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 210 is 3
Notice that 3 = HCF(210,3) .
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Frequently Asked Questions on HCF of 240, 312, 21, 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 240, 312, 21, 210?
Answer: HCF of 240, 312, 21, 210 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 240, 312, 21, 210 using Euclid's Algorithm?
Answer: For arbitrary numbers 240, 312, 21, 210 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.