Highest Common Factor of 487, 672, 560, 107 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 487, 672, 560, 107 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 487, 672, 560, 107 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 487, 672, 560, 107 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 487, 672, 560, 107 is 1.
HCF(487, 672, 560, 107) = 1
HCF of 487, 672, 560, 107 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 487, 672, 560, 107 is 1.
Highest Common Factor of 487,672,560,107 is 1
Step 1: Since 672 > 487, we apply the division lemma to 672 and 487, to get
672 = 487 x 1 + 185
Step 2: Since the reminder 487 ≠ 0, we apply division lemma to 185 and 487, to get
487 = 185 x 2 + 117
Step 3: We consider the new divisor 185 and the new remainder 117, and apply the division lemma to get
185 = 117 x 1 + 68
We consider the new divisor 117 and the new remainder 68,and apply the division lemma to get
117 = 68 x 1 + 49
We consider the new divisor 68 and the new remainder 49,and apply the division lemma to get
68 = 49 x 1 + 19
We consider the new divisor 49 and the new remainder 19,and apply the division lemma to get
49 = 19 x 2 + 11
We consider the new divisor 19 and the new remainder 11,and apply the division lemma to get
19 = 11 x 1 + 8
We consider the new divisor 11 and the new remainder 8,and apply the division lemma to get
11 = 8 x 1 + 3
We consider the new divisor 8 and the new remainder 3,and apply the division lemma to get
8 = 3 x 2 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 487 and 672 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(11,8) = HCF(19,11) = HCF(49,19) = HCF(68,49) = HCF(117,68) = HCF(185,117) = HCF(487,185) = HCF(672,487) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 560 > 1, we apply the division lemma to 560 and 1, to get
560 = 1 x 560 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 560 is 1
Notice that 1 = HCF(560,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 107 > 1, we apply the division lemma to 107 and 1, to get
107 = 1 x 107 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 107 is 1
Notice that 1 = HCF(107,1) .
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Frequently Asked Questions on HCF of 487, 672, 560, 107 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 487, 672, 560, 107?
Answer: HCF of 487, 672, 560, 107 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 487, 672, 560, 107 using Euclid's Algorithm?
Answer: For arbitrary numbers 487, 672, 560, 107 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.