Highest Common Factor of 372, 987, 84 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 372, 987, 84 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 372, 987, 84 is 3 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 372, 987, 84 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 372, 987, 84 is 3.
HCF(372, 987, 84) = 3
HCF of 372, 987, 84 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 372, 987, 84 is 3.
Highest Common Factor of 372,987,84 is 3
Step 1: Since 987 > 372, we apply the division lemma to 987 and 372, to get
987 = 372 x 2 + 243
Step 2: Since the reminder 372 ≠ 0, we apply division lemma to 243 and 372, to get
372 = 243 x 1 + 129
Step 3: We consider the new divisor 243 and the new remainder 129, and apply the division lemma to get
243 = 129 x 1 + 114
We consider the new divisor 129 and the new remainder 114,and apply the division lemma to get
129 = 114 x 1 + 15
We consider the new divisor 114 and the new remainder 15,and apply the division lemma to get
114 = 15 x 7 + 9
We consider the new divisor 15 and the new remainder 9,and apply the division lemma to get
15 = 9 x 1 + 6
We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get
9 = 6 x 1 + 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 372 and 987 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(15,9) = HCF(114,15) = HCF(129,114) = HCF(243,129) = HCF(372,243) = HCF(987,372) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 84 > 3, we apply the division lemma to 84 and 3, to get
84 = 3 x 28 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 84 is 3
Notice that 3 = HCF(84,3) .
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Frequently Asked Questions on HCF of 372, 987, 84 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 372, 987, 84?
Answer: HCF of 372, 987, 84 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 372, 987, 84 using Euclid's Algorithm?
Answer: For arbitrary numbers 372, 987, 84 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.