Highest Common Factor of 126, 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 126, 870 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 126, 870 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 126, 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 126, 870 is 6.
HCF(126, 870) = 6
HCF of 126, 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 126, 870 is 6.
Highest Common Factor of 126,870 is 6
Step 1: Since 870 > 126, we apply the division lemma to 870 and 126, to get
870 = 126 x 6 + 114
Step 2: Since the reminder 126 ≠ 0, we apply division lemma to 114 and 126, to get
126 = 114 x 1 + 12
Step 3: We consider the new divisor 114 and the new remainder 12, and apply the division lemma to get
114 = 12 x 9 + 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 126 and 870 is 6
Notice that 6 = HCF(12,6) = HCF(114,12) = HCF(126,114) = HCF(870,126) .
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Frequently Asked Questions on HCF of 126, 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 126, 870?
Answer: HCF of 126, 870 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 126, 870 using Euclid's Algorithm?
Answer: For arbitrary numbers 126, 870 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.