Highest Common Factor of 542, 892 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 542, 892 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 542, 892 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 542, 892 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 542, 892 is 2.
HCF(542, 892) = 2
HCF of 542, 892 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 542, 892 is 2.
Highest Common Factor of 542,892 is 2
Step 1: Since 892 > 542, we apply the division lemma to 892 and 542, to get
892 = 542 x 1 + 350
Step 2: Since the reminder 542 ≠ 0, we apply division lemma to 350 and 542, to get
542 = 350 x 1 + 192
Step 3: We consider the new divisor 350 and the new remainder 192, and apply the division lemma to get
350 = 192 x 1 + 158
We consider the new divisor 192 and the new remainder 158,and apply the division lemma to get
192 = 158 x 1 + 34
We consider the new divisor 158 and the new remainder 34,and apply the division lemma to get
158 = 34 x 4 + 22
We consider the new divisor 34 and the new remainder 22,and apply the division lemma to get
34 = 22 x 1 + 12
We consider the new divisor 22 and the new remainder 12,and apply the division lemma to get
22 = 12 x 1 + 10
We consider the new divisor 12 and the new remainder 10,and apply the division lemma to get
12 = 10 x 1 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 542 and 892 is 2
Notice that 2 = HCF(10,2) = HCF(12,10) = HCF(22,12) = HCF(34,22) = HCF(158,34) = HCF(192,158) = HCF(350,192) = HCF(542,350) = HCF(892,542) .
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Frequently Asked Questions on HCF of 542, 892 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 542, 892?
Answer: HCF of 542, 892 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 542, 892 using Euclid's Algorithm?
Answer: For arbitrary numbers 542, 892 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.