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 985, 754, 42 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 985, 754, 42 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 985, 754, 42 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 985, 754, 42 is 1.
HCF(985, 754, 42) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 985, 754, 42 is 1.
Step 1: Since 985 > 754, we apply the division lemma to 985 and 754, to get
985 = 754 x 1 + 231
Step 2: Since the reminder 754 ≠ 0, we apply division lemma to 231 and 754, to get
754 = 231 x 3 + 61
Step 3: We consider the new divisor 231 and the new remainder 61, and apply the division lemma to get
231 = 61 x 3 + 48
We consider the new divisor 61 and the new remainder 48,and apply the division lemma to get
61 = 48 x 1 + 13
We consider the new divisor 48 and the new remainder 13,and apply the division lemma to get
48 = 13 x 3 + 9
We consider the new divisor 13 and the new remainder 9,and apply the division lemma to get
13 = 9 x 1 + 4
We consider the new divisor 9 and the new remainder 4,and apply the division lemma to get
9 = 4 x 2 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 985 and 754 is 1
Notice that 1 = HCF(4,1) = HCF(9,4) = HCF(13,9) = HCF(48,13) = HCF(61,48) = HCF(231,61) = HCF(754,231) = HCF(985,754) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 42 > 1, we apply the division lemma to 42 and 1, to get
42 = 1 x 42 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 42 is 1
Notice that 1 = HCF(42,1) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 985, 754, 42?
Answer: HCF of 985, 754, 42 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 985, 754, 42 using Euclid's Algorithm?
Answer: For arbitrary numbers 985, 754, 42 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.