Highest Common Factor of 90, 585, 754 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 90, 585, 754 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 90, 585, 754 is 1 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 90, 585, 754 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 90, 585, 754 is 1.
HCF(90, 585, 754) = 1
HCF of 90, 585, 754 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 90, 585, 754 is 1.
Highest Common Factor of 90,585,754 is 1
Step 1: Since 585 > 90, we apply the division lemma to 585 and 90, to get
585 = 90 x 6 + 45
Step 2: Since the reminder 90 ≠ 0, we apply division lemma to 45 and 90, to get
90 = 45 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 45, the HCF of 90 and 585 is 45
Notice that 45 = HCF(90,45) = HCF(585,90) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 754 > 45, we apply the division lemma to 754 and 45, to get
754 = 45 x 16 + 34
Step 2: Since the reminder 45 ≠ 0, we apply division lemma to 34 and 45, to get
45 = 34 x 1 + 11
Step 3: We consider the new divisor 34 and the new remainder 11, and apply the division lemma to get
34 = 11 x 3 + 1
We consider the new divisor 11 and the new remainder 1, and apply the division lemma to get
11 = 1 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 45 and 754 is 1
Notice that 1 = HCF(11,1) = HCF(34,11) = HCF(45,34) = HCF(754,45) .
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Frequently Asked Questions on HCF of 90, 585, 754 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 90, 585, 754?
Answer: HCF of 90, 585, 754 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 90, 585, 754 using Euclid's Algorithm?
Answer: For arbitrary numbers 90, 585, 754 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.