Highest Common Factor of 510, 900, 962, 692 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 510, 900, 962, 692 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 510, 900, 962, 692 is 2 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 510, 900, 962, 692 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 510, 900, 962, 692 is 2.
HCF(510, 900, 962, 692) = 2
HCF of 510, 900, 962, 692 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 510, 900, 962, 692 is 2.
Highest Common Factor of 510,900,962,692 is 2
Step 1: Since 900 > 510, we apply the division lemma to 900 and 510, to get
900 = 510 x 1 + 390
Step 2: Since the reminder 510 ≠ 0, we apply division lemma to 390 and 510, to get
510 = 390 x 1 + 120
Step 3: We consider the new divisor 390 and the new remainder 120, and apply the division lemma to get
390 = 120 x 3 + 30
We consider the new divisor 120 and the new remainder 30, and apply the division lemma to get
120 = 30 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 30, the HCF of 510 and 900 is 30
Notice that 30 = HCF(120,30) = HCF(390,120) = HCF(510,390) = HCF(900,510) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 962 > 30, we apply the division lemma to 962 and 30, to get
962 = 30 x 32 + 2
Step 2: Since the reminder 30 ≠ 0, we apply division lemma to 2 and 30, to get
30 = 2 x 15 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 30 and 962 is 2
Notice that 2 = HCF(30,2) = HCF(962,30) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 692 > 2, we apply the division lemma to 692 and 2, to get
692 = 2 x 346 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 692 is 2
Notice that 2 = HCF(692,2) .
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Frequently Asked Questions on HCF of 510, 900, 962, 692 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 510, 900, 962, 692?
Answer: HCF of 510, 900, 962, 692 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 510, 900, 962, 692 using Euclid's Algorithm?
Answer: For arbitrary numbers 510, 900, 962, 692 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.