Highest Common Factor of 975, 600 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 975, 600 i.e. 75 the largest integer that leaves a remainder zero for all numbers.
HCF of 975, 600 is 75 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 975, 600 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 975, 600 is 75.
HCF(975, 600) = 75
HCF of 975, 600 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 975, 600 is 75.
Highest Common Factor of 975,600 is 75
Step 1: Since 975 > 600, we apply the division lemma to 975 and 600, to get
975 = 600 x 1 + 375
Step 2: Since the reminder 600 ≠ 0, we apply division lemma to 375 and 600, to get
600 = 375 x 1 + 225
Step 3: We consider the new divisor 375 and the new remainder 225, and apply the division lemma to get
375 = 225 x 1 + 150
We consider the new divisor 225 and the new remainder 150,and apply the division lemma to get
225 = 150 x 1 + 75
We consider the new divisor 150 and the new remainder 75,and apply the division lemma to get
150 = 75 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 75, the HCF of 975 and 600 is 75
Notice that 75 = HCF(150,75) = HCF(225,150) = HCF(375,225) = HCF(600,375) = HCF(975,600) .
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Frequently Asked Questions on HCF of 975, 600 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 975, 600?
Answer: HCF of 975, 600 is 75 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 975, 600 using Euclid's Algorithm?
Answer: For arbitrary numbers 975, 600 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.