Highest Common Factor of 542, 870, 224 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, 870, 224 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 542, 870, 224 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, 870, 224 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, 870, 224 is 2.
HCF(542, 870, 224) = 2
HCF of 542, 870, 224 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, 870, 224 is 2.
Highest Common Factor of 542,870,224 is 2
Step 1: Since 870 > 542, we apply the division lemma to 870 and 542, to get
870 = 542 x 1 + 328
Step 2: Since the reminder 542 ≠ 0, we apply division lemma to 328 and 542, to get
542 = 328 x 1 + 214
Step 3: We consider the new divisor 328 and the new remainder 214, and apply the division lemma to get
328 = 214 x 1 + 114
We consider the new divisor 214 and the new remainder 114,and apply the division lemma to get
214 = 114 x 1 + 100
We consider the new divisor 114 and the new remainder 100,and apply the division lemma to get
114 = 100 x 1 + 14
We consider the new divisor 100 and the new remainder 14,and apply the division lemma to get
100 = 14 x 7 + 2
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 542 and 870 is 2
Notice that 2 = HCF(14,2) = HCF(100,14) = HCF(114,100) = HCF(214,114) = HCF(328,214) = HCF(542,328) = HCF(870,542) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 224 > 2, we apply the division lemma to 224 and 2, to get
224 = 2 x 112 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 224 is 2
Notice that 2 = HCF(224,2) .
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Frequently Asked Questions on HCF of 542, 870, 224 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, 870, 224?
Answer: HCF of 542, 870, 224 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 542, 870, 224 using Euclid's Algorithm?
Answer: For arbitrary numbers 542, 870, 224 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.