Highest Common Factor of 975, 560, 470 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 975, 560, 470 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 975, 560, 470 is 5 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 975, 560, 470 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 975, 560, 470 is 5.
HCF(975, 560, 470) = 5
HCF of 975, 560, 470 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 975, 560, 470 is 5.
Highest Common Factor of 975,560,470 is 5
Step 1: Since 975 > 560, we apply the division lemma to 975 and 560, to get
975 = 560 x 1 + 415
Step 2: Since the reminder 560 ≠ 0, we apply division lemma to 415 and 560, to get
560 = 415 x 1 + 145
Step 3: We consider the new divisor 415 and the new remainder 145, and apply the division lemma to get
415 = 145 x 2 + 125
We consider the new divisor 145 and the new remainder 125,and apply the division lemma to get
145 = 125 x 1 + 20
We consider the new divisor 125 and the new remainder 20,and apply the division lemma to get
125 = 20 x 6 + 5
We consider the new divisor 20 and the new remainder 5,and apply the division lemma to get
20 = 5 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 975 and 560 is 5
Notice that 5 = HCF(20,5) = HCF(125,20) = HCF(145,125) = HCF(415,145) = HCF(560,415) = HCF(975,560) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 470 > 5, we apply the division lemma to 470 and 5, to get
470 = 5 x 94 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 5 and 470 is 5
Notice that 5 = HCF(470,5) .
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Frequently Asked Questions on HCF of 975, 560, 470 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 975, 560, 470?
Answer: HCF of 975, 560, 470 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 975, 560, 470 using Euclid's Algorithm?
Answer: For arbitrary numbers 975, 560, 470 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
