Highest Common Factor of 144, 522 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, 522 i.e. 18 the largest integer that leaves a remainder zero for all numbers.
HCF of 144, 522 is 18 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, 522 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, 522 is 18.
HCF(144, 522) = 18
HCF of 144, 522 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, 522 is 18.
Highest Common Factor of 144,522 is 18
Step 1: Since 522 > 144, we apply the division lemma to 522 and 144, to get
522 = 144 x 3 + 90
Step 2: Since the reminder 144 ≠ 0, we apply division lemma to 90 and 144, to get
144 = 90 x 1 + 54
Step 3: We consider the new divisor 90 and the new remainder 54, and apply the division lemma to get
90 = 54 x 1 + 36
We consider the new divisor 54 and the new remainder 36,and apply the division lemma to get
54 = 36 x 1 + 18
We consider the new divisor 36 and the new remainder 18,and apply the division lemma to get
36 = 18 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 18, the HCF of 144 and 522 is 18
Notice that 18 = HCF(36,18) = HCF(54,36) = HCF(90,54) = HCF(144,90) = HCF(522,144) .
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Frequently Asked Questions on HCF of 144, 522 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, 522?
Answer: HCF of 144, 522 is 18 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 144, 522 using Euclid's Algorithm?
Answer: For arbitrary numbers 144, 522 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.