Highest Common Factor of 372, 696, 986 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, 696, 986 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 372, 696, 986 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 372, 696, 986 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, 696, 986 is 2.
HCF(372, 696, 986) = 2
HCF of 372, 696, 986 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, 696, 986 is 2.
Highest Common Factor of 372,696,986 is 2
Step 1: Since 696 > 372, we apply the division lemma to 696 and 372, to get
696 = 372 x 1 + 324
Step 2: Since the reminder 372 ≠ 0, we apply division lemma to 324 and 372, to get
372 = 324 x 1 + 48
Step 3: We consider the new divisor 324 and the new remainder 48, and apply the division lemma to get
324 = 48 x 6 + 36
We consider the new divisor 48 and the new remainder 36,and apply the division lemma to get
48 = 36 x 1 + 12
We consider the new divisor 36 and the new remainder 12,and apply the division lemma to get
36 = 12 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 372 and 696 is 12
Notice that 12 = HCF(36,12) = HCF(48,36) = HCF(324,48) = HCF(372,324) = HCF(696,372) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 986 > 12, we apply the division lemma to 986 and 12, to get
986 = 12 x 82 + 2
Step 2: Since the reminder 12 ≠ 0, we apply division lemma to 2 and 12, to get
12 = 2 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 12 and 986 is 2
Notice that 2 = HCF(12,2) = HCF(986,12) .
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Frequently Asked Questions on HCF of 372, 696, 986 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, 696, 986?
Answer: HCF of 372, 696, 986 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 372, 696, 986 using Euclid's Algorithm?
Answer: For arbitrary numbers 372, 696, 986 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.