Highest Common Factor of 362, 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 362, 224 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 362, 224 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 362, 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 362, 224 is 2.
HCF(362, 224) = 2
HCF of 362, 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 362, 224 is 2.
Highest Common Factor of 362,224 is 2
Step 1: Since 362 > 224, we apply the division lemma to 362 and 224, to get
362 = 224 x 1 + 138
Step 2: Since the reminder 224 ≠ 0, we apply division lemma to 138 and 224, to get
224 = 138 x 1 + 86
Step 3: We consider the new divisor 138 and the new remainder 86, and apply the division lemma to get
138 = 86 x 1 + 52
We consider the new divisor 86 and the new remainder 52,and apply the division lemma to get
86 = 52 x 1 + 34
We consider the new divisor 52 and the new remainder 34,and apply the division lemma to get
52 = 34 x 1 + 18
We consider the new divisor 34 and the new remainder 18,and apply the division lemma to get
34 = 18 x 1 + 16
We consider the new divisor 18 and the new remainder 16,and apply the division lemma to get
18 = 16 x 1 + 2
We consider the new divisor 16 and the new remainder 2,and apply the division lemma to get
16 = 2 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 362 and 224 is 2
Notice that 2 = HCF(16,2) = HCF(18,16) = HCF(34,18) = HCF(52,34) = HCF(86,52) = HCF(138,86) = HCF(224,138) = HCF(362,224) .
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Frequently Asked Questions on HCF of 362, 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 362, 224?
Answer: HCF of 362, 224 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 362, 224 using Euclid's Algorithm?
Answer: For arbitrary numbers 362, 224 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.