Highest Common Factor of 234, 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 234, 560, 470 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 234, 560, 470 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 234, 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 234, 560, 470 is 2.
HCF(234, 560, 470) = 2
HCF of 234, 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 234, 560, 470 is 2.
Highest Common Factor of 234,560,470 is 2
Step 1: Since 560 > 234, we apply the division lemma to 560 and 234, to get
560 = 234 x 2 + 92
Step 2: Since the reminder 234 ≠ 0, we apply division lemma to 92 and 234, to get
234 = 92 x 2 + 50
Step 3: We consider the new divisor 92 and the new remainder 50, and apply the division lemma to get
92 = 50 x 1 + 42
We consider the new divisor 50 and the new remainder 42,and apply the division lemma to get
50 = 42 x 1 + 8
We consider the new divisor 42 and the new remainder 8,and apply the division lemma to get
42 = 8 x 5 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 234 and 560 is 2
Notice that 2 = HCF(8,2) = HCF(42,8) = HCF(50,42) = HCF(92,50) = HCF(234,92) = HCF(560,234) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 470 > 2, we apply the division lemma to 470 and 2, to get
470 = 2 x 235 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 470 is 2
Notice that 2 = HCF(470,2) .
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Frequently Asked Questions on HCF of 234, 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 234, 560, 470?
Answer: HCF of 234, 560, 470 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 234, 560, 470 using Euclid's Algorithm?
Answer: For arbitrary numbers 234, 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.