Highest Common Factor of 5970, 2142 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 5970, 2142 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 5970, 2142 is 6 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 5970, 2142 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 5970, 2142 is 6.
HCF(5970, 2142) = 6
HCF of 5970, 2142 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 5970, 2142 is 6.
Highest Common Factor of 5970,2142 is 6
Step 1: Since 5970 > 2142, we apply the division lemma to 5970 and 2142, to get
5970 = 2142 x 2 + 1686
Step 2: Since the reminder 2142 ≠ 0, we apply division lemma to 1686 and 2142, to get
2142 = 1686 x 1 + 456
Step 3: We consider the new divisor 1686 and the new remainder 456, and apply the division lemma to get
1686 = 456 x 3 + 318
We consider the new divisor 456 and the new remainder 318,and apply the division lemma to get
456 = 318 x 1 + 138
We consider the new divisor 318 and the new remainder 138,and apply the division lemma to get
318 = 138 x 2 + 42
We consider the new divisor 138 and the new remainder 42,and apply the division lemma to get
138 = 42 x 3 + 12
We consider the new divisor 42 and the new remainder 12,and apply the division lemma to get
42 = 12 x 3 + 6
We consider the new divisor 12 and the new remainder 6,and apply the division lemma to get
12 = 6 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 5970 and 2142 is 6
Notice that 6 = HCF(12,6) = HCF(42,12) = HCF(138,42) = HCF(318,138) = HCF(456,318) = HCF(1686,456) = HCF(2142,1686) = HCF(5970,2142) .
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Frequently Asked Questions on HCF of 5970, 2142 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 5970, 2142?
Answer: HCF of 5970, 2142 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 5970, 2142 using Euclid's Algorithm?
Answer: For arbitrary numbers 5970, 2142 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.