Highest Common Factor of 224, 304, 510 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, 304, 510 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 224, 304, 510 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, 304, 510 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, 304, 510 is 2.
HCF(224, 304, 510) = 2
HCF of 224, 304, 510 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, 304, 510 is 2.
Highest Common Factor of 224,304,510 is 2
Step 1: Since 304 > 224, we apply the division lemma to 304 and 224, to get
304 = 224 x 1 + 80
Step 2: Since the reminder 224 ≠ 0, we apply division lemma to 80 and 224, to get
224 = 80 x 2 + 64
Step 3: We consider the new divisor 80 and the new remainder 64, and apply the division lemma to get
80 = 64 x 1 + 16
We consider the new divisor 64 and the new remainder 16, and apply the division lemma to get
64 = 16 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 16, the HCF of 224 and 304 is 16
Notice that 16 = HCF(64,16) = HCF(80,64) = HCF(224,80) = HCF(304,224) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 510 > 16, we apply the division lemma to 510 and 16, to get
510 = 16 x 31 + 14
Step 2: Since the reminder 16 ≠ 0, we apply division lemma to 14 and 16, to get
16 = 14 x 1 + 2
Step 3: We consider the new divisor 14 and the new remainder 2, and apply the division lemma to get
14 = 2 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 16 and 510 is 2
Notice that 2 = HCF(14,2) = HCF(16,14) = HCF(510,16) .
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Frequently Asked Questions on HCF of 224, 304, 510 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, 304, 510?
Answer: HCF of 224, 304, 510 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 224, 304, 510 using Euclid's Algorithm?
Answer: For arbitrary numbers 224, 304, 510 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.