Highest Common Factor of 144, 560, 638 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 144, 560, 638 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 144, 560, 638 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 144, 560, 638 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 144, 560, 638 is 2.
HCF(144, 560, 638) = 2
HCF of 144, 560, 638 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 144, 560, 638 is 2.
Highest Common Factor of 144,560,638 is 2
Step 1: Since 560 > 144, we apply the division lemma to 560 and 144, to get
560 = 144 x 3 + 128
Step 2: Since the reminder 144 ≠ 0, we apply division lemma to 128 and 144, to get
144 = 128 x 1 + 16
Step 3: We consider the new divisor 128 and the new remainder 16, and apply the division lemma to get
128 = 16 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 16, the HCF of 144 and 560 is 16
Notice that 16 = HCF(128,16) = HCF(144,128) = HCF(560,144) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 638 > 16, we apply the division lemma to 638 and 16, to get
638 = 16 x 39 + 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 638 is 2
Notice that 2 = HCF(14,2) = HCF(16,14) = HCF(638,16) .
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Frequently Asked Questions on HCF of 144, 560, 638 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 144, 560, 638?
Answer: HCF of 144, 560, 638 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 144, 560, 638 using Euclid's Algorithm?
Answer: For arbitrary numbers 144, 560, 638 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.