Highest Common Factor of 224, 578, 132 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 224, 578, 132 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 224, 578, 132 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 224, 578, 132 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 224, 578, 132 is 2.
HCF(224, 578, 132) = 2
HCF of 224, 578, 132 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 224, 578, 132 is 2.
Highest Common Factor of 224,578,132 is 2
Step 1: Since 578 > 224, we apply the division lemma to 578 and 224, to get
578 = 224 x 2 + 130
Step 2: Since the reminder 224 ≠ 0, we apply division lemma to 130 and 224, to get
224 = 130 x 1 + 94
Step 3: We consider the new divisor 130 and the new remainder 94, and apply the division lemma to get
130 = 94 x 1 + 36
We consider the new divisor 94 and the new remainder 36,and apply the division lemma to get
94 = 36 x 2 + 22
We consider the new divisor 36 and the new remainder 22,and apply the division lemma to get
36 = 22 x 1 + 14
We consider the new divisor 22 and the new remainder 14,and apply the division lemma to get
22 = 14 x 1 + 8
We consider the new divisor 14 and the new remainder 8,and apply the division lemma to get
14 = 8 x 1 + 6
We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get
8 = 6 x 1 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 224 and 578 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(14,8) = HCF(22,14) = HCF(36,22) = HCF(94,36) = HCF(130,94) = HCF(224,130) = HCF(578,224) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 132 > 2, we apply the division lemma to 132 and 2, to get
132 = 2 x 66 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 132 is 2
Notice that 2 = HCF(132,2) .
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Frequently Asked Questions on HCF of 224, 578, 132 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 224, 578, 132?
Answer: HCF of 224, 578, 132 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 224, 578, 132 using Euclid's Algorithm?
Answer: For arbitrary numbers 224, 578, 132 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.