Highest Common Factor of 902, 546, 870 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 902, 546, 870 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 902, 546, 870 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 902, 546, 870 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 902, 546, 870 is 2.
HCF(902, 546, 870) = 2
HCF of 902, 546, 870 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 902, 546, 870 is 2.
Highest Common Factor of 902,546,870 is 2
Step 1: Since 902 > 546, we apply the division lemma to 902 and 546, to get
902 = 546 x 1 + 356
Step 2: Since the reminder 546 ≠ 0, we apply division lemma to 356 and 546, to get
546 = 356 x 1 + 190
Step 3: We consider the new divisor 356 and the new remainder 190, and apply the division lemma to get
356 = 190 x 1 + 166
We consider the new divisor 190 and the new remainder 166,and apply the division lemma to get
190 = 166 x 1 + 24
We consider the new divisor 166 and the new remainder 24,and apply the division lemma to get
166 = 24 x 6 + 22
We consider the new divisor 24 and the new remainder 22,and apply the division lemma to get
24 = 22 x 1 + 2
We consider the new divisor 22 and the new remainder 2,and apply the division lemma to get
22 = 2 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 902 and 546 is 2
Notice that 2 = HCF(22,2) = HCF(24,22) = HCF(166,24) = HCF(190,166) = HCF(356,190) = HCF(546,356) = HCF(902,546) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 870 > 2, we apply the division lemma to 870 and 2, to get
870 = 2 x 435 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 870 is 2
Notice that 2 = HCF(870,2) .
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Frequently Asked Questions on HCF of 902, 546, 870 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 902, 546, 870?
Answer: HCF of 902, 546, 870 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 902, 546, 870 using Euclid's Algorithm?
Answer: For arbitrary numbers 902, 546, 870 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
