Highest Common Factor of 562, 912 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 562, 912 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 562, 912 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 562, 912 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 562, 912 is 2.
HCF(562, 912) = 2
HCF of 562, 912 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 562, 912 is 2.
Highest Common Factor of 562,912 is 2
Step 1: Since 912 > 562, we apply the division lemma to 912 and 562, to get
912 = 562 x 1 + 350
Step 2: Since the reminder 562 ≠ 0, we apply division lemma to 350 and 562, to get
562 = 350 x 1 + 212
Step 3: We consider the new divisor 350 and the new remainder 212, and apply the division lemma to get
350 = 212 x 1 + 138
We consider the new divisor 212 and the new remainder 138,and apply the division lemma to get
212 = 138 x 1 + 74
We consider the new divisor 138 and the new remainder 74,and apply the division lemma to get
138 = 74 x 1 + 64
We consider the new divisor 74 and the new remainder 64,and apply the division lemma to get
74 = 64 x 1 + 10
We consider the new divisor 64 and the new remainder 10,and apply the division lemma to get
64 = 10 x 6 + 4
We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get
10 = 4 x 2 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 562 and 912 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(64,10) = HCF(74,64) = HCF(138,74) = HCF(212,138) = HCF(350,212) = HCF(562,350) = HCF(912,562) .
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Frequently Asked Questions on HCF of 562, 912 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 562, 912?
Answer: HCF of 562, 912 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 562, 912 using Euclid's Algorithm?
Answer: For arbitrary numbers 562, 912 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.