Highest Common Factor of 356, 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 356, 224 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 356, 224 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 356, 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 356, 224 is 4.
HCF(356, 224) = 4
HCF of 356, 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 356, 224 is 4.
Highest Common Factor of 356,224 is 4
Step 1: Since 356 > 224, we apply the division lemma to 356 and 224, to get
356 = 224 x 1 + 132
Step 2: Since the reminder 224 ≠ 0, we apply division lemma to 132 and 224, to get
224 = 132 x 1 + 92
Step 3: We consider the new divisor 132 and the new remainder 92, and apply the division lemma to get
132 = 92 x 1 + 40
We consider the new divisor 92 and the new remainder 40,and apply the division lemma to get
92 = 40 x 2 + 12
We consider the new divisor 40 and the new remainder 12,and apply the division lemma to get
40 = 12 x 3 + 4
We consider the new divisor 12 and the new remainder 4,and apply the division lemma to get
12 = 4 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 356 and 224 is 4
Notice that 4 = HCF(12,4) = HCF(40,12) = HCF(92,40) = HCF(132,92) = HCF(224,132) = HCF(356,224) .
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Frequently Asked Questions on HCF of 356, 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 356, 224?
Answer: HCF of 356, 224 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 356, 224 using Euclid's Algorithm?
Answer: For arbitrary numbers 356, 224 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.