Highest Common Factor of 840, 465, 616, 450 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 840, 465, 616, 450 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 840, 465, 616, 450 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 840, 465, 616, 450 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 840, 465, 616, 450 is 1.
HCF(840, 465, 616, 450) = 1
HCF of 840, 465, 616, 450 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 840, 465, 616, 450 is 1.
Highest Common Factor of 840,465,616,450 is 1
Step 1: Since 840 > 465, we apply the division lemma to 840 and 465, to get
840 = 465 x 1 + 375
Step 2: Since the reminder 465 ≠ 0, we apply division lemma to 375 and 465, to get
465 = 375 x 1 + 90
Step 3: We consider the new divisor 375 and the new remainder 90, and apply the division lemma to get
375 = 90 x 4 + 15
We consider the new divisor 90 and the new remainder 15, and apply the division lemma to get
90 = 15 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 840 and 465 is 15
Notice that 15 = HCF(90,15) = HCF(375,90) = HCF(465,375) = HCF(840,465) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 616 > 15, we apply the division lemma to 616 and 15, to get
616 = 15 x 41 + 1
Step 2: Since the reminder 15 ≠ 0, we apply division lemma to 1 and 15, to get
15 = 1 x 15 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 15 and 616 is 1
Notice that 1 = HCF(15,1) = HCF(616,15) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 450 > 1, we apply the division lemma to 450 and 1, to get
450 = 1 x 450 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 450 is 1
Notice that 1 = HCF(450,1) .
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Frequently Asked Questions on HCF of 840, 465, 616, 450 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 840, 465, 616, 450?
Answer: HCF of 840, 465, 616, 450 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 840, 465, 616, 450 using Euclid's Algorithm?
Answer: For arbitrary numbers 840, 465, 616, 450 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.