Highest Common Factor of 196, 324 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 196, 324 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 196, 324 is 4 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 196, 324 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 196, 324 is 4.
HCF(196, 324) = 4
HCF of 196, 324 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 196, 324 is 4.
Highest Common Factor of 196,324 is 4
Step 1: Since 324 > 196, we apply the division lemma to 324 and 196, to get
324 = 196 x 1 + 128
Step 2: Since the reminder 196 ≠ 0, we apply division lemma to 128 and 196, to get
196 = 128 x 1 + 68
Step 3: We consider the new divisor 128 and the new remainder 68, and apply the division lemma to get
128 = 68 x 1 + 60
We consider the new divisor 68 and the new remainder 60,and apply the division lemma to get
68 = 60 x 1 + 8
We consider the new divisor 60 and the new remainder 8,and apply the division lemma to get
60 = 8 x 7 + 4
We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 196 and 324 is 4
Notice that 4 = HCF(8,4) = HCF(60,8) = HCF(68,60) = HCF(128,68) = HCF(196,128) = HCF(324,196) .
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Frequently Asked Questions on HCF of 196, 324 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 196, 324?
Answer: HCF of 196, 324 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 196, 324 using Euclid's Algorithm?
Answer: For arbitrary numbers 196, 324 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.