Highest Common Factor of 630, 914, 270, 16 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 630, 914, 270, 16 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 630, 914, 270, 16 is 2 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 630, 914, 270, 16 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 630, 914, 270, 16 is 2.
HCF(630, 914, 270, 16) = 2
HCF of 630, 914, 270, 16 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 630, 914, 270, 16 is 2.
Highest Common Factor of 630,914,270,16 is 2
Step 1: Since 914 > 630, we apply the division lemma to 914 and 630, to get
914 = 630 x 1 + 284
Step 2: Since the reminder 630 ≠ 0, we apply division lemma to 284 and 630, to get
630 = 284 x 2 + 62
Step 3: We consider the new divisor 284 and the new remainder 62, and apply the division lemma to get
284 = 62 x 4 + 36
We consider the new divisor 62 and the new remainder 36,and apply the division lemma to get
62 = 36 x 1 + 26
We consider the new divisor 36 and the new remainder 26,and apply the division lemma to get
36 = 26 x 1 + 10
We consider the new divisor 26 and the new remainder 10,and apply the division lemma to get
26 = 10 x 2 + 6
We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get
10 = 6 x 1 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 630 and 914 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(26,10) = HCF(36,26) = HCF(62,36) = HCF(284,62) = HCF(630,284) = HCF(914,630) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 270 > 2, we apply the division lemma to 270 and 2, to get
270 = 2 x 135 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 270 is 2
Notice that 2 = HCF(270,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 16 > 2, we apply the division lemma to 16 and 2, to get
16 = 2 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 16 is 2
Notice that 2 = HCF(16,2) .
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Frequently Asked Questions on HCF of 630, 914, 270, 16 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 630, 914, 270, 16?
Answer: HCF of 630, 914, 270, 16 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 630, 914, 270, 16 using Euclid's Algorithm?
Answer: For arbitrary numbers 630, 914, 270, 16 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.