Highest Common Factor of 180, 987, 784, 10 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 180, 987, 784, 10 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 180, 987, 784, 10 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 180, 987, 784, 10 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 180, 987, 784, 10 is 1.
HCF(180, 987, 784, 10) = 1
HCF of 180, 987, 784, 10 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 180, 987, 784, 10 is 1.
Highest Common Factor of 180,987,784,10 is 1
Step 1: Since 987 > 180, we apply the division lemma to 987 and 180, to get
987 = 180 x 5 + 87
Step 2: Since the reminder 180 ≠ 0, we apply division lemma to 87 and 180, to get
180 = 87 x 2 + 6
Step 3: We consider the new divisor 87 and the new remainder 6, and apply the division lemma to get
87 = 6 x 14 + 3
We consider the new divisor 6 and the new remainder 3, and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 180 and 987 is 3
Notice that 3 = HCF(6,3) = HCF(87,6) = HCF(180,87) = HCF(987,180) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 784 > 3, we apply the division lemma to 784 and 3, to get
784 = 3 x 261 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 784 is 1
Notice that 1 = HCF(3,1) = HCF(784,3) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 10 > 1, we apply the division lemma to 10 and 1, to get
10 = 1 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 10 is 1
Notice that 1 = HCF(10,1) .
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Frequently Asked Questions on HCF of 180, 987, 784, 10 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 180, 987, 784, 10?
Answer: HCF of 180, 987, 784, 10 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 180, 987, 784, 10 using Euclid's Algorithm?
Answer: For arbitrary numbers 180, 987, 784, 10 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.