Highest Common Factor of 700, 960 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 700, 960 i.e. 20 the largest integer that leaves a remainder zero for all numbers.
HCF of 700, 960 is 20 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 700, 960 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 700, 960 is 20.
HCF(700, 960) = 20
HCF of 700, 960 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 700, 960 is 20.
Highest Common Factor of 700,960 is 20
Step 1: Since 960 > 700, we apply the division lemma to 960 and 700, to get
960 = 700 x 1 + 260
Step 2: Since the reminder 700 ≠ 0, we apply division lemma to 260 and 700, to get
700 = 260 x 2 + 180
Step 3: We consider the new divisor 260 and the new remainder 180, and apply the division lemma to get
260 = 180 x 1 + 80
We consider the new divisor 180 and the new remainder 80,and apply the division lemma to get
180 = 80 x 2 + 20
We consider the new divisor 80 and the new remainder 20,and apply the division lemma to get
80 = 20 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 20, the HCF of 700 and 960 is 20
Notice that 20 = HCF(80,20) = HCF(180,80) = HCF(260,180) = HCF(700,260) = HCF(960,700) .
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Frequently Asked Questions on HCF of 700, 960 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 700, 960?
Answer: HCF of 700, 960 is 20 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 700, 960 using Euclid's Algorithm?
Answer: For arbitrary numbers 700, 960 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.