Highest Common Factor of 975, 762 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, 762 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 975, 762 is 3 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, 762 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, 762 is 3.
HCF(975, 762) = 3
HCF of 975, 762 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, 762 is 3.
Highest Common Factor of 975,762 is 3
Step 1: Since 975 > 762, we apply the division lemma to 975 and 762, to get
975 = 762 x 1 + 213
Step 2: Since the reminder 762 ≠ 0, we apply division lemma to 213 and 762, to get
762 = 213 x 3 + 123
Step 3: We consider the new divisor 213 and the new remainder 123, and apply the division lemma to get
213 = 123 x 1 + 90
We consider the new divisor 123 and the new remainder 90,and apply the division lemma to get
123 = 90 x 1 + 33
We consider the new divisor 90 and the new remainder 33,and apply the division lemma to get
90 = 33 x 2 + 24
We consider the new divisor 33 and the new remainder 24,and apply the division lemma to get
33 = 24 x 1 + 9
We consider the new divisor 24 and the new remainder 9,and apply the division lemma to get
24 = 9 x 2 + 6
We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get
9 = 6 x 1 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 975 and 762 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(24,9) = HCF(33,24) = HCF(90,33) = HCF(123,90) = HCF(213,123) = HCF(762,213) = HCF(975,762) .
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Frequently Asked Questions on HCF of 975, 762 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, 762?
Answer: HCF of 975, 762 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 975, 762 using Euclid's Algorithm?
Answer: For arbitrary numbers 975, 762 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.