Highest Common Factor of 570, 882, 118, 15 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 570, 882, 118, 15 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 570, 882, 118, 15 is 1 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 570, 882, 118, 15 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 570, 882, 118, 15 is 1.
HCF(570, 882, 118, 15) = 1
HCF of 570, 882, 118, 15 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 570, 882, 118, 15 is 1.
Highest Common Factor of 570,882,118,15 is 1
Step 1: Since 882 > 570, we apply the division lemma to 882 and 570, to get
882 = 570 x 1 + 312
Step 2: Since the reminder 570 ≠ 0, we apply division lemma to 312 and 570, to get
570 = 312 x 1 + 258
Step 3: We consider the new divisor 312 and the new remainder 258, and apply the division lemma to get
312 = 258 x 1 + 54
We consider the new divisor 258 and the new remainder 54,and apply the division lemma to get
258 = 54 x 4 + 42
We consider the new divisor 54 and the new remainder 42,and apply the division lemma to get
54 = 42 x 1 + 12
We consider the new divisor 42 and the new remainder 12,and apply the division lemma to get
42 = 12 x 3 + 6
We consider the new divisor 12 and the new remainder 6,and apply the division lemma to get
12 = 6 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 570 and 882 is 6
Notice that 6 = HCF(12,6) = HCF(42,12) = HCF(54,42) = HCF(258,54) = HCF(312,258) = HCF(570,312) = HCF(882,570) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 118 > 6, we apply the division lemma to 118 and 6, to get
118 = 6 x 19 + 4
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 4 and 6, to get
6 = 4 x 1 + 2
Step 3: 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 6 and 118 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(118,6) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 15 > 2, we apply the division lemma to 15 and 2, to get
15 = 2 x 7 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 15 is 1
Notice that 1 = HCF(2,1) = HCF(15,2) .
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Frequently Asked Questions on HCF of 570, 882, 118, 15 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 570, 882, 118, 15?
Answer: HCF of 570, 882, 118, 15 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 570, 882, 118, 15 using Euclid's Algorithm?
Answer: For arbitrary numbers 570, 882, 118, 15 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.