Highest Common Factor of 704, 450 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 704, 450 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 704, 450 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 704, 450 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 704, 450 is 2.
HCF(704, 450) = 2
HCF of 704, 450 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 704, 450 is 2.
Highest Common Factor of 704,450 is 2
Step 1: Since 704 > 450, we apply the division lemma to 704 and 450, to get
704 = 450 x 1 + 254
Step 2: Since the reminder 450 ≠ 0, we apply division lemma to 254 and 450, to get
450 = 254 x 1 + 196
Step 3: We consider the new divisor 254 and the new remainder 196, and apply the division lemma to get
254 = 196 x 1 + 58
We consider the new divisor 196 and the new remainder 58,and apply the division lemma to get
196 = 58 x 3 + 22
We consider the new divisor 58 and the new remainder 22,and apply the division lemma to get
58 = 22 x 2 + 14
We consider the new divisor 22 and the new remainder 14,and apply the division lemma to get
22 = 14 x 1 + 8
We consider the new divisor 14 and the new remainder 8,and apply the division lemma to get
14 = 8 x 1 + 6
We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get
8 = 6 x 1 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 704 and 450 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(14,8) = HCF(22,14) = HCF(58,22) = HCF(196,58) = HCF(254,196) = HCF(450,254) = HCF(704,450) .
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Frequently Asked Questions on HCF of 704, 450 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 704, 450?
Answer: HCF of 704, 450 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 704, 450 using Euclid's Algorithm?
Answer: For arbitrary numbers 704, 450 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
