Highest Common Factor of 96, 336, 224 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 96, 336, 224 i.e. 16 the largest integer that leaves a remainder zero for all numbers.
HCF of 96, 336, 224 is 16 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 96, 336, 224 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 96, 336, 224 is 16.
HCF(96, 336, 224) = 16
HCF of 96, 336, 224 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 96, 336, 224 is 16.
Highest Common Factor of 96,336,224 is 16
Step 1: Since 336 > 96, we apply the division lemma to 336 and 96, to get
336 = 96 x 3 + 48
Step 2: Since the reminder 96 ≠ 0, we apply division lemma to 48 and 96, to get
96 = 48 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 48, the HCF of 96 and 336 is 48
Notice that 48 = HCF(96,48) = HCF(336,96) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 224 > 48, we apply the division lemma to 224 and 48, to get
224 = 48 x 4 + 32
Step 2: Since the reminder 48 ≠ 0, we apply division lemma to 32 and 48, to get
48 = 32 x 1 + 16
Step 3: We consider the new divisor 32 and the new remainder 16, and apply the division lemma to get
32 = 16 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 16, the HCF of 48 and 224 is 16
Notice that 16 = HCF(32,16) = HCF(48,32) = HCF(224,48) .
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Frequently Asked Questions on HCF of 96, 336, 224 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 96, 336, 224?
Answer: HCF of 96, 336, 224 is 16 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 96, 336, 224 using Euclid's Algorithm?
Answer: For arbitrary numbers 96, 336, 224 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.