Highest Common Factor of 455, 574, 875 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 455, 574, 875 i.e. 7 the largest integer that leaves a remainder zero for all numbers.
HCF of 455, 574, 875 is 7 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 455, 574, 875 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 455, 574, 875 is 7.
HCF(455, 574, 875) = 7
HCF of 455, 574, 875 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 455, 574, 875 is 7.
Highest Common Factor of 455,574,875 is 7
Step 1: Since 574 > 455, we apply the division lemma to 574 and 455, to get
574 = 455 x 1 + 119
Step 2: Since the reminder 455 ≠ 0, we apply division lemma to 119 and 455, to get
455 = 119 x 3 + 98
Step 3: We consider the new divisor 119 and the new remainder 98, and apply the division lemma to get
119 = 98 x 1 + 21
We consider the new divisor 98 and the new remainder 21,and apply the division lemma to get
98 = 21 x 4 + 14
We consider the new divisor 21 and the new remainder 14,and apply the division lemma to get
21 = 14 x 1 + 7
We consider the new divisor 14 and the new remainder 7,and apply the division lemma to get
14 = 7 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 455 and 574 is 7
Notice that 7 = HCF(14,7) = HCF(21,14) = HCF(98,21) = HCF(119,98) = HCF(455,119) = HCF(574,455) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 875 > 7, we apply the division lemma to 875 and 7, to get
875 = 7 x 125 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 7 and 875 is 7
Notice that 7 = HCF(875,7) .
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Frequently Asked Questions on HCF of 455, 574, 875 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 455, 574, 875?
Answer: HCF of 455, 574, 875 is 7 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 455, 574, 875 using Euclid's Algorithm?
Answer: For arbitrary numbers 455, 574, 875 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.