Highest Common Factor of 2170, 1300 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 2170, 1300 i.e. 10 the largest integer that leaves a remainder zero for all numbers.
HCF of 2170, 1300 is 10 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 2170, 1300 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 2170, 1300 is 10.
HCF(2170, 1300) = 10
HCF of 2170, 1300 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2170, 1300 is 10.
Highest Common Factor of 2170,1300 is 10
Step 1: Since 2170 > 1300, we apply the division lemma to 2170 and 1300, to get
2170 = 1300 x 1 + 870
Step 2: Since the reminder 1300 ≠ 0, we apply division lemma to 870 and 1300, to get
1300 = 870 x 1 + 430
Step 3: We consider the new divisor 870 and the new remainder 430, and apply the division lemma to get
870 = 430 x 2 + 10
We consider the new divisor 430 and the new remainder 10, and apply the division lemma to get
430 = 10 x 43 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 2170 and 1300 is 10
Notice that 10 = HCF(430,10) = HCF(870,430) = HCF(1300,870) = HCF(2170,1300) .
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Frequently Asked Questions on HCF of 2170, 1300 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 2170, 1300?
Answer: HCF of 2170, 1300 is 10 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2170, 1300 using Euclid's Algorithm?
Answer: For arbitrary numbers 2170, 1300 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.